Lesson 5: Practice Problems

Problem 1

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

$2 (x + 5) = 3 x + 1$
$3 y - 4 = 6 - 2 y$
$3 (n + 2) = 9 (6 - n)$

Problem 2

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Clare’s mistake and what is the solution to the equation?

$\begin{aligned} 12 (5 + 2 y) & = 4 y - (5 - 9 y) \\ 72 + 24 y & = 4 y - 5 - 9 y \\ 72 + 24 y & = - 5 y - 5 \\ 24 y & = - 5 y - 77 \\ 29 y & = - 77 \\ y & = \frac{- 77}{29} \end{aligned}$

Problem 3

Solve each equation, and check your solution.

$\frac{1}{9} (2 m - 16) = \frac{1}{3} (2 m + 4)$
$- 4 (r + 2) = 4 (2 - 2 r)$
$12 (5 + 2 y) = 4 y - (6 - 9 y)$

Problem 4 From Unit 3 Lesson 13

Here is the graph of a linear equation.

A graph on a coordinate grid with a point at (-1,1) and it crosses the y axis at (0,1.25)

Select all true statements about the line and its equation.

One solution of the equation is $(3, 2)$ .
One solution of the equation is $(- 1, 1)$ .
One solution of the equation is $(1, \frac{3}{2})$ .
There are 2 solutions.
There are infinitely many solutions.
The equation of the line is $y = \frac{1}{4} x + \frac{5}{4}$ .
The equation of the line is $y = \frac{5}{4} x + \frac{1}{4}$ .

Problem 5 From Unit 3 Lesson 9

A participant in a 21-mile walkathon walks at a steady rate of 3 miles per hour. He thinks, “The relationship between the number of miles left to walk and the number of hours I already walked can be represented by a line with slope $- 3$ .” Do you agree with his claim? Explain your reasoning.