Expressions, Equations and Inequalities Guided Notes Standards: Alg1.M.A.SSE.A.01a - The Highly Proficient student can explain the context of different parts of a formula presented as a complicated expression. Alg1.M.A.REI.B.03 - The Highly Proficient student can create, solve and graph linear equations and inequalities in one variable. Objective 1: I can identify and explain parts of an expression and can explain the difference between and expression and an equation. Algebraic Expressions: Definition: Examples: Parts of Expressions: Variable: Constant: Term: Coefficient: Like Terms: For the expression 7x 2 + 12+ 5y - 6x 5 + 8y list all variables, constants, terms, coefficients and like terms Algebraic Equations: Definition: Examples: What is the key different between algebraic expression and algebraic equations? 1
Writing Expressions: Verbal expressions can be translated to numerical or algebraic expressions by identifying numerical values, variables, and key terms that signal an operation. Key Words: Addition Subtraction Multiplication Division Write an algebraic expression for each phrase. a) Seven more than n b) The difference of n and 7 c) The product of 7 and n d) The quotient of n and 7 Example Three: Define a variable and write an algebraic expression for each phrase. a) Two times a number plus 5 b) 7 less than three times a number Writing Equations: Writing equations from verbal description is very similar to writing expression, however, you will be writing two expressions that are set equal to each other. In everyday language, the word is suggests an equals sign. Example Four: Define a variable and write an algebraic equation for each phrase. a) 3 less than a number squared is the same as five b) The quotient of fifty and five more than a number is ten Homework: 2
Objective 2: I can solve one-step and two-step equations. Solving Equations: Solving an equation means finding all the values of the variable that make the equation a true statement. One-Step Equations: A one-step equation is a type of equation that only requires one step to solve! These equations can be simply solved by identifying the operation you see happening in the equation, then applying the inverse operation. Solve each one-step equation by applying the inverse operation. a) 21 + q = 29 b) m 48 = 29 c) -13s = 195 d) t/30 = 7 Two-Step Equations A two-step equation is a type of equation that requires two steps to solve. Typically, these two steps are 1) 2) Solve each two-step equation. a) 10x + 7 = 37 b) 10 = m/4 + 2 c) (x + 4)/3 = 2 Homework: 3
Objective 3: I can solve multi-step equations using the distributive property and combining like terms and I can apply equations to solve real-world problems. Distributive Property: a(b + c) = (a + b)c = a(b c) = (a b)c = Simplify using the distributive property a) 5(x + 2) = b) (3 y)(-7) = c) 6(3y + 4) 3(5 2x) = Combining Like-Terms: Like terms have the same variable raised to the same power. To combine them, you combine their coefficients. Simplify by combining like terms. a) 2x + 3y 4x 7y + 9xy 7xy b) x + 1 + x2 + 4x + 4 c) 4(2 + x) 2(x + 3) = 4 Multi-Step Equations: Multi-step equations are equations that require more than two steps to solve. You will need to use a combination of inverse operations, the distributive property and combing like terms to solve these. Example Three: Solve each multi step equation using combining like terms and the distributive property. a) 4b + 16 + 2b = 46 b) -2(b 4) = 12 Example Four: Solve each multi-step equation that contains fraction or decimals. a) 2x/3 + x/2 = 7 b) 0.5a + 8.75 = 13.25 4
Objective 4: I can solve and graph the solution to multi-step inequalities and use them to solve realworld problems. Inequalities: Definition: The Inequality Symbols and their Graphs: There are four inequality symbols, each with their own unique meaning. < means > means means means Interval Notation: Interval notation is a common way that mathematicians represent a portion of a number line, often times connected to an inequality. This communicates the same information as graphing the solution to an inequality, but is much easier to write. Interval notation uses a combination of brackets [ ], parenthesis () and commas to represent parts of the number line, or intervals. Graph each inequality and write the equivalent interval notation. 5
Solving Inequalities: A solution of an inequality is any number that makes the inequality true. For example, the solution of the inequality x < 3 are all numbers that less than 3. Inequalities are solved much the same way you would solve an equation. Instead of having just one solution, inequalities actually have infinitely many solutions, so it is not possible to check all the solutions. However, you can check your work by plugging one of the possible solutions to see if you get a correct statement. Solve each one-step inequality. Graph your solution and write it in interval notation. a) x 3 < 5 b) -5z 25 Example Three: Solve each two-step inequality. Graph your solution and write is in interval notation. a) 2x 3 < 1 b) 7 + 6a 19 Example Four: Solve each multi-step inequality. Graph your solution and write is in interval notation. a) 2(t + 2) 3t -1 b) -3(4 m) 2(4m 14) Homework: 6