Lesson 13: Practice Problems

Problem 1

Mai and Tyler work on the equation $\frac{2}{5} b + 1 = - 11$ together. Mai’s solution is $b = - 25$ and Tyler’s is $b = - 28$ . Here is their work:

Mai:
$\frac{2}{5} b + 1 = - 11$
$\frac{2}{5} b = - 10$
$b = - 10 \cdot \frac{5}{2}$
$b = - 25$

Tyler:
$\frac{2}{5} b + 1 = - 11$
$2 b + 1 = - 55$
$2 b = - 56$
$b = - 28$

Do you agree with their solutions? Explain or show your reasoning.

Problem 2

Solve $3 (x - 4) = 12 x$

Problem 3

Describe what is being done in each step while solving the equation.

$2 (- 3 x + 4) = 5 x + 2$
$- 6 x + 8 = 5 x + 2$
$8 = 11 x + 2$
$6 = 11 x$
$x = \frac{6}{11}$

Problem 4

Andre solved an equation, but when he checked his answer he saw his solution was incorrect. He knows he made a mistake, but he can’t find it. Where is Andre’s mistake and what is the solution to the equation?

$\begin{aligned} - 2 (3 x - 5) & = 4 (x + 3) + 8 \\ - 6 x + 10 & = 4 x + 12 + 8 \\ - 6 x + 10 & = 4 x + 20 \\ 10 & = - 2 x + 20 \\ - 10 & = - 2 x \\ 5 & = x \end{aligned}$