Solving Equations With Rational Numbers

Transcription

1 Solving Equations With Rational Numbers Solving one Step Equations with Rational Numbers Solve linear equations in one variable. CC.8.EE.7 Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). CC.8.EE.7a Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. CC.8.EE.7b Lesson objectives Teachers' notes 1

2 Addition Property of Equality Words: Adding the same number to each side of an equation produces an equivalent equation. Algebra: if a = b, then a + c = b + c Subtraction Property of Equality Words: Subtracting the same number to each side of an equation produces an equivalent equation. Algebra: if a = b, then a - c = b - c Multiplication Property of Equality Words: Multiplying the same number to each side of an equation produces an equivalent equation. Algebra: if a = b, then a c = b c Division Property of Equality Words: Dividing the same number to each side of an equation produces an equivalent equation. Algebra: if a = b, then a - c = b - c 2

3 Solving Equations Containing Rational Numbers Adding and Subtracting to Solve Equations 1) Add 3 to each side. 2) Subtract 6 to from side. Solving Equations Containing Rational Numbers Adding and Subtracting to Solve Equations 3) Add to each side. 4) The variable is already isolated. 3

4 Solving Equations Containing Rational Numbers Adding and Subtracting to Solve Equations 5) Subtract -8.7 from each side. 6) Add 3.7 to each side. Solving Equations Containing Rational Numbers Adding and Subtracting to Solve Equations 7) 4

5 Check Point 1) 2) 3) 4) d = 3 Solving Equations Containing integers Multiplying and Dividing to Solve Equations 1) Divide both sides by - 5. x 1 1 x 2) Multiply both sides by

6 Solving Equations Containing integers Multiplying and Dividing to Solve Equations 3) Multiply both sides by 4) Multiply both sides by 1.2. Solving Equations Containing integers Multiplying and Dividing to Solve Equations 5) x = 6 Divide both sides by 6

7 Check Point 11) 12) 13) 14) Solving Equations Containing integers 1) 2) 3) 4) 7

8 Problem Solving 2-4 Solving Equations Containing integers 5) Sarah heard on the morning news that the temperature had dropped 26 degrees since midnight. In the morning, the temperature was -8 F. What was the temperature at midnight? Write and solve an equation. Verbal Model: Write an equation Solve an equation 2-4 Solving Equations Containing integers Problem Solving 6) The sum of the measures of the interior angles of the parallelogram is 360 o. Write and solve an equation to find the value of the variable. Write an equation 35 o + x + x + 35 o = 360 o. Solve an equation 35 o + x + x + 35 o = 360 o. 2x + 70 o = 360 o -70 o -70 o 2x = 290 o 2 2 x = 145 o 8

9 Check Point A roller coaster descends a hill at a rate of 80 feet per second. The bottom of the hill is 400 feet from the top. How long will it take the coaster riders to reach the bottom? Write and solve an equation. 80r = 400 r = 5 It will take the roller coaster 5 seconds to reach the bottom. 9