Lesson 6

Strategic Solving

Let's solve linear equations like a boss.

Problem 1

Solve each of these equations. Explain or show your reasoning.

2b+8-5b+3=\text-13+8b-5

2x+7-5x+8=3(5+6x)-12x

2c-3=2(6-c)+7c

Problem 2

Solve each equation and check your solution.

\text-3w-4=w+3

3(3-3x)=2(x+3)-30

\frac13(z+4)-6=\frac23(5-z)

Problem 3

Elena said the equation 9x+15=3x+15 has no solutions because 9x is greater than 3x. Do you agree with Elena? Explain your reasoning.

Problem 4

The table gives some sample data for two quantities, x and y, that are in a proportional relationship.

  1. Complete the table.
  2. Write an equation that represents the relationship between x and y shown in the table.
  3. Graph the relationship. Use a scale for the axes that shows all the points in the table.

x y
14 21
64
39
1
Blank coordinate plane.
(From Unit 3, Lesson 3.)