Lesson 7: Practice Problems

Problem 1

For each equation, decide if it is always true or never true.

$x - 13 = x + 1$
$x + \frac{1}{2} = x - \frac{1}{2}$
$2 (x + 3) = 5 x + 6 - 3 x$
$x - 3 = 2 x - 3 - x$
$3 (x - 5) = 2 (x - 5) + x$

Problem 2

Mai says that the equation $2 x + 2 = x + 1$ has no solution because the left hand side is double the right hand side. Do you agree with Mai? Explain your reasoning.

Problem 3

Write the other side of this equation so it’s true for all values of $x$ : $\frac{1}{2} (6 x - 10) - x =$
Write the other side of this equation so it’s true for no values of $x$ : $\frac{1}{2} (6 x - 10) - x =$

Problem 4

Here is an equation that is true for all values of $x$ : $5 (x + 2) = 5 x + 10$ . Elena saw this equation and says she can tell $20 (x + 2) + 31 = 4 (5 x + 10) + 31$ is also true for any value of $x$ . How can she tell? Explain your reasoning.

Problem 5 From Unit 4 Lesson 4

Elena and Lin are trying to solve $\frac{1}{2} x + 3 = \frac{7}{2} x + 5$ . Describe the change they each make to each side of the equation.

Elena’s first step is to write $3 = \frac{7}{2} x - \frac{1}{2} x + 5$ .
Lin’s first step is to write $x + 6 = 7 x + 10$ .

Problem 6 From Unit 4 Lesson 6

Solve each equation and check your solution.

$3 x - 6 = 4 (2 - 3 x) - 8 x$
$\frac{1}{2} z + 6 = \frac{3}{2} (z + 6)$
$9 - 7 w = 8 w + 8$

Problem 7 From Unit 3 Lesson 12

The point $(- 3, 6)$ is on a line with a slope of 4.

Find two more points on the line.
Write an equation for the line.