Lesson 6: Practice Problems

Problem 1

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

$2 b + 8 - 5 b + 3 = - 13 + 8 b - 5$
$2 x + 7 - 5 x + 8 = 3 (5 + 6 x) - 12 x$
$2 c - 3 = 2 (6 - c) + 7 c$

Problem 2

Solve each equation and check your solution.

$- 3 w - 4 = w + 3$
$3 (3 - 3 x) = 2 (x + 3) - 30$
$\frac{1}{3} (z + 4) - 6 = \frac{2}{3} (5 - z)$

Problem 3

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

Problem 4 From Unit 3 Lesson 3

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

Complete the table.
$x$
$y$
$14$
$21$
$64$
$39$
$1$
Write an equation that represents the relationship between $x$ and $y$ shown in the table.
Graph the relationship. Use a scale for the axes that shows all the points in the table.