Download - Lesson 6: Solutions of a Linear EquationLesson 6 8•4 Lesson 6 : Solutions of a Linear Equation S.21 Problem Set Transform the equation if necessary, and then solve it to find the

8•4 Lesson 6

Lesson 6: Solutions of a Linear Equation


Classwork Exercises

Find the value of 𝑥𝑥 that makes the equation true. 1. 17 − 5(2𝑥𝑥 − 9) = −(−6𝑥𝑥 + 10) + 4

2. −(𝑥𝑥 − 7) + 53 = 2(𝑥𝑥 + 9)

A STORY OF RATIOS

This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka- math.orgG8-M4-SE-1.3.0-07.2015

S.18

8•4 Lesson 6


3. 49

+ 4(𝑥𝑥 − 1) = 289− (𝑥𝑥 − 7𝑥𝑥) + 1

4. 5(3𝑥𝑥 + 4) − 2𝑥𝑥 = 7𝑥𝑥 − 3(−2𝑥𝑥 + 11)

A STORY OF RATIOS


S.19

8•4 Lesson 6


5. 7𝑥𝑥 − (3𝑥𝑥 + 5) − 8 = 12 (8𝑥𝑥 + 20) − 7𝑥𝑥 + 5

6. Write at least three equations that have no solution.

A STORY OF RATIOS


S.20

8•4 Lesson 6


Problem Set Transform the equation if necessary, and then solve it to find the value of 𝑥𝑥 that makes the equation true.

1. 𝑥𝑥 − (9𝑥𝑥 − 10) + 11 = 12𝑥𝑥 + 3 �−2𝑥𝑥 + 13�

2. 7𝑥𝑥 + 8 �𝑥𝑥 + 14� = 3(6𝑥𝑥 − 9) − 8

3. −4𝑥𝑥 − 2(8𝑥𝑥 + 1) = −(−2𝑥𝑥 − 10)

4. 11(𝑥𝑥 + 10) = 132

5. 37𝑥𝑥 + 12 − �𝑥𝑥 +14� = 9(4𝑥𝑥 − 7) + 5

6. 3(2𝑥𝑥 − 14) + 𝑥𝑥 = 15 − (−9𝑥𝑥 − 5)

7. 8(2𝑥𝑥 + 9) = 56

Lesson Summary

The distributive property is used to expand expressions. For example, the expression 2(3𝑥𝑥 − 10) is rewritten as 6𝑥𝑥 − 20 after the distributive property is applied.

The distributive property is used to simplify expressions. For example, the expression 7𝑥𝑥 + 11𝑥𝑥 is rewritten as (7 + 11)𝑥𝑥 and 18𝑥𝑥 after the distributive property is applied.

The distributive property is applied only to terms within a group:

4(3𝑥𝑥 + 5) − 2 = 12𝑥𝑥 + 20 − 2.

Notice that the term −2 is not part of the group and, therefore, not multiplied by 4.

When an equation is transformed into an untrue sentence, such as 5 ≠ 11, we say the equation has no solution.

A STORY OF RATIOS


S.21