Lesson 6

Strategic Solving

The practice problem answers are available at one of our IM Certified Partners

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 Grade8, Unit 3, Lesson 3.)