UNIT 2 SOLVING EQUATIONS
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1 UNIT 2 SOLVING EQUATIONS NAME: GRADE: TEACHER: Ms. Schmidt _
2 Solving One and Two Step Equations The goal of solving equations is to. We do so by using. *Remember, whatever you to do one side of an equation. 5 Steps to Solve a Two Step Equation 1. Identify x. 2. Preform an operation on BOTH sides 3. Draw a line 4. Write what s left over 5. Repeat until x is isolated Examples: (Solve for the variable) 1) 2x + 8 = 20 2) x 2 3 = 27 3) 13 = 3x 8 4) x = -4 5) a = 22 6) 19 6y = 21 7) 6 + a = 8 8) -x + 3 = ) -3 4x = ) x = ) 14 = y ) 4 x = ) If you multiply John s age by 4 and then subtract 2, you get 10. What is John s age? 14) Multiply Joe s age by 4, then add 2, and you get 22. What is Joe s age?
3 Solving One and Two Step Equations 15) A taxi charges $2.50 a ride plus $1.25 per mile traveled. If the total charge for one ride was $8.75, how many miles were traveled? 16) Mary s age is 5 years less than half Katie s age. If Marie is 11 years old, how old is Katie? Solve for the Variable 1) 3x + 7 = -11 2) -2x + 6 = -8 3) x = 9 4) -4k 8 = 20 5) 4 = 9g 50 6) 8 + 2a = -34 7) -4 = -10 2e 8) -6 4w = -18 9) 5 + n 7 = -9 10) x + 2 = -1 11) 18 = -4w 6 12) -k + 5 = -8 9
4 Solving One and Two Step Equations Solve for the Variable 1) 6x - 1 = 19 2) 2x + 12 = 18 3) -8 = a 4) x = 9 5) x 3 21 = -56 6) 77 = 10a + 7 7) 5a 35 = 0 8) 4r + 13 = 41 9) 4 posters cost $7.40. If each poster costs the same, how much does each poster cost? 10) If you double your weight and add 6, your weight is 200 lbs. How much do you weigh?
5 Solving Equations with Like Terms VOCABULARY 1) Like Terms. Examples: *Combine like terms on each side of the equal sign, then solve the remaining two step equation. Examples: (Solve for the variable) 1) 2x + 5x = 28 2) a 14 = 1 3) 6x + 4 8x = -34 4) 4a + 9a 6a = 42 5) 5x 12 6x = 9 6) 4x x + 1 = 22 7) 7x 5 + 3x = 15 8) 12 = 3c c Write an equation and solve 9) If you sell 3 bags of candy, then 4 bags and finally 1 bag, how much is each bag if you collected $6.40? Classwork: (Solve for the variable) 1) 13a 6a = 49 2) y + 2y = 12 3) 9 4a + 4 = -3 4) 6y 4y + y = 18 5) 13x 7 5x = 9 6) 18 = 8y 7 3y 7) 32 = -8x x 8) 9m + 5 4m = 35 Write an equation and solve 9) We rent 3 video games on Friday and 11 on Saturday. Each video game costs the same amount. If we spend $8.40, how much was each game?
6 Solving Equations with Like Terms Solve for the Variable 1) 3a + 6a = 90 2) 3y y + 4y = -36 3) a a = ) 8x + 7 5x = 31 5) 6 = w ) 5y + 2y 9y = -84 Write an equation and solve 7) Leo bought two pages for his album and Jackie bought three pages. If each page costs the same and together they spent $15, how much did each page cost? 8) The formula for perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. Evaluate the equation if the length of the rectangle is 8 and the width is 3. 9) Simplify the expression: ) Convert 160 C to degrees Fahrenheit Show all work
7 Solving Equations with Variables on Both Sides Steps: 1. Combine like terms on the same side of the equal sign if any. 2. If like terms are separated by an equal sign, bring them together by using inverse operations. Move the variables to one side of the equal sign and the constants to the other side. 3. Solve the remaining two step equation. Examples: (Solve for the variable) 1) 4x 2 = x 5 2) 2x 6 = 14 3x 3) 18x + x = 5x 7 4) 11 a = -1 7a 5) -4y 1 + 9y = y 6) 7x + 8 = 4x ) x = 10x ) 4y + 11 = -y + 7 Write an equation and solve 9) You have $12.50 in a savings account. You deposit $7.25 more each week. Your friend has $32.50 in a savings account. She deposits $5.25 more each week. In how many weeks will they have the same amount? Classwork: (Solve for the variable) 1) 4x + 17 = 7x + 8 2) 3x x = x 3) 6x 3 = 7x x 4) -5x = 4x ) 12 n = n 6) 8k 36 = -4k 7) 7k 5 8k = 4 + k - 6 8) 8 g = g + 5
8 Solving Equations with Variables on Both Sides Solve each equation 1) 9y 7 = 5y ) n = n 3) 14x + 9 = x 4) 7k 11 = k 5) y 3 13 = -11 6) x = x ) 4 = 4x + 3x 10 8) 8k 36 = -4k 9) Marcy made an error when solving the equation below. 8m 20 = 36 8m = 36 8m = 36 8m = m = A) Identify Marcy s error to explain why it resulted in an incorrect solution. B) Correctly solve 8m 20 = 36 for m. Show your work. 10) Evaluate: If x = 2 and y = -3: 11) What value of x make the equation true? -3xy x + y 2 ¾ x + 9 = 3 A. x = -8 B. x = -½ C. x = 1 D. x = 16
9 Solving Equations with the Distributive Property VOCABULARY 1) Distribute STEPS 1) Distribute to clear the parenthesis 2) Combine like terms on each side of the equal sign 3) Perform inverse (Opposite) operations 4) Solve the remaining two step equation. Examples: (Solve for the variable) 1) 2(x + 6) = 20 2) 3(5x + 10) = 90 3) 3(x 5) = 2(2x + 1) 4) 2(x - 5) = -3(6x 10) 5) 2x = 10(x 4) 6) 5(x + 6) = 3x 7) 8(x 1) = 4(x + 4) 8) 7(2a 4) = 2(a + 4) Classwork: (Solve for the variable) 1) 4(x 2) = 20 2) -5(x + 4) = 15 3) 2 (6+ 2a) = 24 4) 7(3x 4) = 14 5) 7(x + 1) = 9 + 5x 6) 4(y 1) = 2y + 6 7) 3(x 3) = x + 1 8) 2(4 + 6x) = 2(5x + 7)
10 Solving Equations with the Distributive Property Homework: Solve each equation. 1) 4(x 1) = 20 2) 2(5 + x) = 22 3) -5(x + 4) = 15 4) 5(a + 4) = 10 5) -4(2m + 6) = 16 6) 3(2b + 3) = 27 7) 14 a = 2(a + 4) 8) 2(x + 3) = 3(x 3) 9 Which best describes the solution for this equation? 0.5(4x + 3) = 5x 2.5 A. x = 0.75 B. x = 1. 3 C. x = 4 D. x = 12 Convert the following temperatures: 10) 80 C = F 11) 8 3x + 5 If the area of the rectangle is 112, what is the value of x?
11 Solving Multi-Step Equations STEPS 1) Distribute to clear the parenthesis. 2) Combine like terms on each side of the equal sign. 3) Perform inverse (Opposite) operations. 4) Solve the remaining two step equation. Examples: 1) 2(x 4) = 5x x 2) 3(4x 1) 2 = 17x + 10 Classwork: (Solve for the variable) 1) 3(x + 5) + 2x = ) 4(x + 10) + 6x = ) 5(x + 3) = 2x + x ) 2(3x + 4) = 3x + x ) 5(2x + 6) = 5x 10 6) 2(3x 6) = 16 8x 7) Find the value of x so that each pair of polygons has the same perimeter. x + 4 x + 2 x + 1 x + 5 x + 3
12 Solving Multi-Step Equations Solve for x: x 8) 3x + 15 = ) ) x x = ) -4(2x - 4) = 80 12) What value of t make this equation true? 6t 8 = 2(2t + 1) A. t = -3 B. t = 1 C. t = 2 D. t = 5 13) Sylvie s age is 5 years less than half Katie s age. If Sylvie is 11 years old, what is Katie s age? A. 8 years old B. 12 years old C. 27 years old D. 32 years old 6) Is 4 the solution to the equation -2n + 5 = -3? Explain how you know.
13 Solving Multi-Step Equations Simplify 1) 6x + x 2) 5x ) 6x + 2y 4x + y 4) 3(x + 7) 5) -5(2x + 4) 6) Yolanda has $38 in a bank account. She wants to make two equal deposits so that her account will have a balance of $100. How much money does Yolanda need to deposit each time? A. $19 B. $31 C. $38 D. $62 Solve for x: 7) 6(x 2) = 42 8) 3(2x + 4) = 5x ) 6x x = 4x ) -(x + 2) = 8
14 Solving Special Solutions Vocabulary TYPE OF SOLUTIONS Algebraic Form Definition No Solution (none) a = b One Solution (one) x = a Infinite Solutions (many) a = a 2x 4 = 2(x + 1) 2x 4 = -x 1 2x 4 = 2(x 2) 2x 4 = 2x + 2 +x +x 2x 4 = 2x 4-2x -2x 3x 4 = -1-2x -2x -4 = 2 (no solution) = -4 (infinite solutions) 3x = x = 1 (one solution) Examples: (Solve for the variable and identify the type of solution) 1) 5x + 8 = 5(x + 3) 2) 9x = 8 + 5x 3) 6x + 12 = 6x ) 7x 11 = 17 7x 5) 4x + 8 = 4(x + 4) 6) 3x + 3 = 3(x + 1) Classwork: (Solve for the variable and identify the type of solution) 1) 5x = 9 + 2x 2) x + 9 = 7x + 9 6x 3) 22y = 11(3 + y) 4) -3y + 1 = y + 9 4y 5) 16z 24 = 8(2z 3) 6) -5w = 7 4w + 8
15 Solving Special Solutions Solve for the variable and identify the type of solution 1) 4r + 7 r = 3(5 + r) 2) 4(x 2) = -2x x 3) 2x + 18 = (x + 9)2 4) 2(5 + x) = 22 5) 6x x = x + 1 6) 9y 24 = 3(3y 8) 7) Which best describes the solution for 5b 25 = 25? 8) Which best describes the solution for the a. no solution equation: 6y 3 = -6y + 3 b. 0 a. no solution c. 10 b. infinitely many solutions d. 80 c. 0.5 d. 2 9) Simplify the following: 10) Using the formula: C = 5 (F 32), 9 4(-3) + 9 (- 3) 7 find C when F = 59 degrees. 11) Combine like terms: -3(x + 7) + 4x 2y y + x
16 Solving Decimal Equations Examples: (Solve for the variable) 1) 0.2x + 0.3x = 25 2) 0.6x = 2.4 3) 0.4a = 55 4) 0.75y y = 85 5) 0.7y = 4.2 6) 0.10x x = 1.9 7) 0.03x = 0.15(4 x) 8) 0.35x = ) A ball player s batting average is this year. This is 1.2 times his average from last year. What was his average from last year? Classwork: (Solve for the variable) 1) 0.4z + 0.8z = 3.6 2) 0.7 = a 3) 0.4a = 55 4) 0.7y + 0.1y = 16 5) 0.3n + 0.9n = 4.8 6) 0.21x + 3.6= x 7) 5.5(2x 3) = 10x 8) 0.2x = 0.2x + 23
17 Solving Decimal Equations Solve for the variable 1) 0.6z + 3z = 3.6z 2) 0.7 = x 3) 0.4c + 0.7c = 55 4) -0.9y - 0.4y = 65 5) -0.12x = x 6) 2.1(15 + n) = 63 7) 4.2z + 1.5z = 57 8) 9 x = 0.4(15 5x) 9) One suitcase is 5.8 kg less than another. Together the two suitcases are 37.6 kg. Find the weight of each suitcase. Perform the indicated value 10) If x = -2 and y = -1 find 11) Using the formula: C = 5 (F 32), 9-3x + 4y - xy find C when F = 5 degrees.
18 Solving Fractional Equations STEPS 1) Put all terms in fraction form if needed. 2) Find a common denominator. 3) Change all terms to a fraction with the common denominator. 4) Cancel out the denominator. 5) Follow steps for solving equations. Examples: (Solve for the variable) 1) 4a 2 a 2 = 6 2) 7x 4 + 2x 4 = 18 3) y 2 y 4 = 5 Solve for the variable 1) 2m = 1 2) x = x 2 3) m = ) (12x 9) 26 5) 2 3 (2x 4) = 1 5x 11 x + 4 6) ) 3x 4 x 4 = -8 8) x 3 + 6x 3 = 14 9) y 3 y 5 = 4
19 Solving Fractional Equations Solve for the variable 1) x 7x 6 6 = 4 2) 3x + 2x 9 9 = 5 3) y + y 6 3 = 6 4) x 5 4 = 2 x 10 5) = x 4 6) 3n 2 + 2n 3 = 13 5x 7) x 1 8) 5 2 9) 2 (8x 3) = x ) The perimeter of a rectangle is 8(2x + 1) inches. If the length of the side of a rectangle is 3x + 4 inches and the width is 4x + 3 inches, what is the length of each side of the rectangle?
20 Aim: I can solve decimal and fractional equations Lesson 5 Warm Up: Quiz A. Decimal Equations 1) 0.75y y = 85 2) 0.02a = 0.7 3) 0.03x = 0.15(0.3 x) 4) 0.4z + 0.8z = 1.2z ) 0.42m + 0.8m = 1.2m 6) 0.4a = 55 7) 0.012x 4 = 0.112x + 1 8) x x = ) 5x x = B. Fractional Equations 1. 1 x + 13 = 1 x (x + 8 ) = x + 5 = 1 4 x 5 6
21 4. x+5 = x 4 3x x 4 3x = 8 6. x+3 = x 8 + 5x x+5 2 x 4 5 = 4 8. x 4 = x 2x x+5 = x 4 + 3x ) a a ) 2x ) d d Homework p.58 #1,2,7,13,14 p.82 #5,6,9,10,12, 13
22 Aim: I can solve proportional equations Lesson 6 Warm Up: 1. x 3 + 3x 2-2x - 5, when x = A. Restrictions on the Denominator Recall that fractions cannot have denominators of zero. Therefore, when given a fraction containing a variable in the denominator, it is correctly written as a compound statement. 5 For example: and x 2 x 2 This is because x + 2 cannot equal 0. Therefore we solve the equation x + 2 = 0 to determine what x cannot be (which in this case is -2). State the restrictions for the each fraction: 1. x+4 4 x x 9 x+2 2x 8 4. x 7 3x x 5x 4 6. x+3 2x 9 B. Solving Proportions 1. What is a proportion? 2. How do we solve proportions? Solve: 3 n w y 3 17 and y and m 0 5 m Write the missing compound statement for each equation, and then solve: c d h 9 h x 2( x 4) x 2 x h 2
23 Proportional Equations HW Lesson 6 State the restrictions for x; then solve the equation x = 4 4x y 5 a 3. 4 a m m x+1 3 = 6x x+1 4 = 44 x 5 7. x 3 2 = x
24 Aim: I can solve literal equations Lesson 8 H 50 Warm Up: Is there a relationship between shoe size and height? The formula = s where s is 2 your shoe size and h is your height in inches, predicts the height of teenagers. Use the formula to find your height using your shoe size. Is it accurate? The relationship between shoe size and height. This formula predicts the height of teenagers, but the predictions should be taken with a grain of salt. Unfortunately, the results you get are far from reliable. Shoe size generally is proportional to height, so it s used in many height-predicting formulations. Many factors ultimately determine a teen s height like gender, hormones, genes, overall health and nutrition. How would it be easier to find your height? How can we get the H by itself? H 50 2 = s Many formulas are literal equations because they contain more than one variable. When multiple variables are involved, and depending what information we have and what we are looking for determine what our equation should look like. For example, if I we are given the area of a many different circles, and want to determine their radius, I would want the equation to read r = not A=
25 Aim: I can solve literal equations Lesson 8 H 50 Warm Up: Is there a relationship between shoe size and height? The formula 2 your shoe size and H is your height in inches, predicts the height of teenagers. = s where S is Use the formula to find your height using your shoe size. Is it accurate? How can we get the H by itself? H 50 2 = s A. Solving Literal Equations 1. A = πr 2 for π 2. V = πr 2 h for h 3. D = rt for r 4. A = 1 2 bh ; h 5. P = 2l + 2w or w 6. F = 9 C + 32 for C 5
26 7. A = 1 2 h(b 1 + b 2 ) for b 2 8. V = 4 3 πr3 for π 9. x + 5r = 7r for x 10. 2x = n(a+1) for a 11. a(x + y) = w for x 12. a + c = b a for a (Show both ways) (Discuss simplifying) 13. r + sy = t for y 14. rsx rs 2 = 0 for x 15. 9x 24a = 6a + 4x for x 16. x+y = w for x ap 17. 2w + 6y = 8x for w 18. V = 1 lwh for h x 5-7 = 2y Homework p #1,2,4, 6-18 even omit #12, 20a
27 Extra Problems 1) The members of the senior class are planning a dance. They use the equation to determine the total receipts. What is n expressed in terms of r and p? 1) 2) 3) 4) 2) The formula for the volume of a pyramid is. What is h expressed in terms of B and V? 1) 2) 3) 4) 3) If, then x equals 1) 2) 3) 4) 4) If, what is y in terms of e, n, k, and t? 1) 2) 3) 4) 5) If, the value of a in terms of b and r can be expressed as 1) 2) 3) 4) 6) If, the value of m in terms of a, k, and x can be expressed as 1) 2) 3) 4) 7) If, what is x expressed in terms of a and b? 1) 2) 3) 4)
28 1) If, then x equals 1) 2) 3) 4) 2) A formula used for calculating velocity is. What is a expressed in terms of v and t? 1) 2) 3) 4) 8) Solve the equation for x. For each step, describe the operation used to convert the equation. 3x [8 3(x 1)] = x x (8 3x + 3) = x x (11 3x) = x x x = x x 11 = x x 11 = 19 5x = 30 x = 6 nx = 4j 5x for x
29 Aim: I can write and graph inequalities Lesson 1 Warm Up: Solve 1. Factor: x 4 +10x Simplify: x + x 3. Simplify: (x)(x) A. Inequalities and Interval notation Symbol Words Graph Interval Notation x<7 x<7 x>7 x>7 x=7 x 7 Graph each of the following and express in interval notation 1) x > 6 2) x = -3 3) x < 0 4) 8 > x 5) x 5 6) x > -3 B. Graphing Compound Inequality is an inequality formed by joining two inequalities with the word and or the word or. 1) -1 < x < 2 2) 4 < x < 8 3) 6 > x > 2 4) x > 0 or x < -2 5) x < -1 or x > 3 6) x > 7 or x < 10
30 C. Writing Inequalities and Express in Interval Notation 7) 8) 9) ) 11) 12) ) 14) Roster form - [4 [ is the same as (4 ( is the same as Examples: 15) Write (-1, 5] in roster form. then in inequality form 16) Write (-2, 4) in roster form. then in inequality form 17) Write [1, 6] in roster form. then in inequality form Write each in roster form Write each as a compound inequality: 18) ( 1, 7] 19) (-, ) 20) [ 3, 9] 21) (2, 11)
31 Writing and Graphing Inequalities Homework Lesson 1 Graph the following inequalities < x < < x < < x < < x 5. x<-2 or x> > x > 0 7. x < x < 8 Write the inequality for each graph and express in interval notation ) Write [2, 9) in roster form. 16) Write (-3, 1) as a compound inequality: For each of the following, write an inequality to represent the interval notation. 17) (4, 9] 18) (-, 0) 19) [3, ) 20) [-12, -6) 21) If x = 2 and y = -3, evaluate: 5x 2y 22) Solve for x: 0.1(5x + 20) 5 = 0.25(2x + 8)
32 Aim: I can solve inequalities Lesson 2 Warm Up: Solve 1. bx = 9b 2 for x 2. 5x = a + w for w 3. ax + b = 3b for b A. Solving Inequalities (2y + 3) 3y x (2x 8) 8x x 4 > 4 + 5x 5. -3x > x > x x x < 7 + 2(x 3) B. Proportional Inequalities Solve and Graph 1) 4x ) x ) x 6 x 4 2 4) x ) x 1 x ) x 9 2x ) x 1 2 x 6 5
33 Solving Inequality Homework Lesson 2 Textbook - p #1-5 and 7, 12, 19, 21 and Problems below *Solve, Graph, and represent the answer using Interval Notation 1) x ) x 7 x 9 6 3) x 9 5 x 6 8 4) x 9 5 x 5 8 5) x 3 4 x 3 4 6) x 2 x The set {1,2,3,4} is equivalent to (1){x 1 < x < 4, where x is a whole number} (2){x 0 < x < 4, where x is a whole number} (3){x 0 < x 4, where x is a whole number} (4){x 1< x 4, where x is a whole number} 8. Which interval notation represents the set of all numbers from -6 through 14, inclusive? (1) (-6,14) (3) [-6,14) (2) (-6,14] (4) [-6,14] 9. Which of the following inequalities represents the graph (1) 2 < x < 7 (2) 2 x 7 (3) 2 x < 7 (4) 2 < x 7
34 Aim: I can solve and graphing compound inequalities Lesson 3 Warm Up: a x > x Subtract 2x2 + 3x 8 from 5x 2 8x + 7 A. Compound Inequalities Compound Inequality is an inequality formed by joining two inequalities with the word and or the word or. And solution must work in BOTH inequalities Or Solutions must work in at least one of the inequalities Solving and Graphing Compound Inequalities 3) 4 < x 5 < 7 4) 3x 5 < -8 or 2x 1 > 5 5) -3 < -2x ) 4x or 3x 5 4 7) x + 8 = 3 or x 6 = 2 8) 2w 8 = 10 and w > 12 9) -3< x+2 3 <7 10) 10 < 5x 5 < 30 11) 5r (r 2)
35 12) Which of these compound inequalities has no solution? (1) x + 1 > 5 or x + 2 < 2 (3) x + 1 < 5 or x + 3 > 2 (2) x + 1 > 5 and x + 2 < 2 (4) x + 1 < 5 and x + 3 > 2 13) Which value of x is in the solution set of the inequality -4x + 2 > 10? (1) -2 (2) 2 (3) 3 (4) Which inequality represents the given graph (1) 2 < x < 2 (2) x < 2 or x 2 (3) x < 2 or x > 2 (4) x > 2 or x < What inequality is defined in interval notation by (-, -2) or [3, + )? (1) x < -2 and x 3 (2) x < -2 or x 3 (3) x -2 or x > 3 (4) -2 < x Which of the following is a solution to the inequality 2x + 4 > 18 (1) 7 (2) -7 (3) 0 (4) What are the solutions of 3d 4 < -10 or 2d + 7 9? A) d > -2 B) d 1 C) -2 < d 1 D) d < -2 or d 1 Homework p.77 #28a, 29b, 30ab, 36, 38
36 Aim: I can solve inequality word problems Lesson 4 Warm Up: x 6 1. For what value of x will the fraction be undefined? x 8 2. Simplify: (3x 4 7x + 3) (-6x 4 + 2x 9) 3. Perry s Pizza Parlor sells pepperoni pizza for $1.15 per piece and plain pizza for $0.90 apiece. Paul purchases 37 pieces of pizza for Pam s party, paying $ Write an equation that can be used to determine the number of pieces of pepperoni pizza Paul sold? A. Translating Inequalities x>12 x 12 x<12 x 12 Represent each sentence as an algebraic inequality 1. x is at most The greatest possible value of 3y is The sum of 5x and 2x is at least The maximum value of 4x 6 is The minimum value of 2x + 1 is 13. B. Word Problems. Express as an inequality and solve. 1. Michael has $53.50 in his pocket and wants to purchase shirts at a sale price of $14.95 each. How many shirts can he buy? 2. The members of the theater club agree to buy at least 255 tickets. If they expect to buy 80 fewer orchestra tickets than balcony tickets, what is the least number of balcony tickets they will buy? 3. The length of a rectangle is 12 cm less than 3 times its width. If the perimeter of the rectangle is at most 104 meters. Find the greatest possible length of the rectangle. 4. Three times a number increased by 8 is at most 40 more than the number. Find the greatest value of the number.
37 6. Mrs. Milano decided that she should spend no more than $110 to buy a jacket and a skirt. If the price of the jacket was $20 more than three times the skirt, find the highest possible price of the skirt. 7. Jerry wants $30 to buy music online. His father agrees to pay him $6 an hour for raking leaves in addition to his $5 weekly allowance for helping around the house. What is the minimum number of full hours Jerry must work on the leaves to receive at least $30 this week? 8. A sugar donut has 110 more calories than twice the number of calories in a slice of whole wheat bread. Together they contain at least 194 calories. What is the smallest possible number of calories in the slice of bread? Homework p.77 #8a,b,c,d,e,j p.80 # 6,7, 9, 13
UNIT 2 SOLVING EQUATIONS
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