Lesson 3 Solving Equations Literally Practice Understanding

Ready

Perform each operation described in the first column of the table on the inequality $- 9 < 2$ . Record the work in the second column. State whether the new inequality is true or false in the third column of the table.

1.

Apply each operation to the original inequality $- 9 < 2$	Result	Is the resulting inequality true or false?
Example: Add $3$ to both sides.	$- 9 + 3 < 2 + 3 \to - 6 < 5$	True
Subtract $7$ from both sides.
Add $15$ to both sides.
Add $- 10$ to both sides.
Multiply both sides by $10$ .
Divide both sides by $5$ .
Multiply both sides by $- 6$ .
Divide both sides by $- 3$ .

2.

What operations performed on an inequality will reverse the inequality?

Set

Solve for the indicated variable. Show your work!

3.

Solve for $m$ .

$y = 7 m + 6$

4.

Solve for $m$ .

$y = m x + b$

5.

Solve for $x$ .

$\frac{x + 2}{7} = 4$

6.

Solve for $x$ .

$\frac{x + 2 y}{7} = 4$

7.

Solve for $x$ .

$\frac{2 x}{5} - 9 = 6$

8.

Solve for $x .$

$\frac{2 x}{5} - 9 y = 6$

9.

Solve for $x$ .

$\frac{3}{4} (x - 2) = 12$

10.

Solve for $x$ .

$\frac{3}{4} (x - 2 y) = 12$

Go

Locate the $x$ -intercept and $y$ -intercept in the table. Write each as an ordered pair.

11.

$x$	$y$
$- 4$	$12$
$- 3$	$10$
$- 2$	$8$
$- 1$	$6$
$0$	$4$
$1$	$2$
$2$	$0$

$x$ -intercept:

$y$ -intercept:

12.

$x$	$y$
$0$	$- 6$
$3$	$- 5$
$6$	$- 4$
$9$	$- 3$
$12$	$- 2$
$15$	$- 1$
$18$	$0$

$x$ -intercept:

$y$ -intercept:

13.

$x$	$y$
$- 3$	$10$
$- 2$	$8$
$- 1$	$6$
$0$	$4$
$1$	$2$
$2$	$0$
$3$	$- 2$

$x$ -intercept:

$y$ -intercept:

Locate the $x$ -intercept and the $y$ -intercept in the graph. Write each as an ordered pair.

14.

$x$ -intercept:

$y$ -intercept:

15.

$x$ -intercept:

$y$ -intercept:

Solve each equation for $x$ . Provide the justifications for each step. See the first example as a reminder for the types of justifications that might be used.

$\begin{array}{cl} 3 x - 6 = 15 & Justification \\ + 6 + 6 & Addition Property of Equality \\ \frac{3 x}{3} = \frac{21}{3} & Division Property of Equality \\ x = 7 \end{array}$

16.

$4 x - 10 = 2$

17.

$- 16 = 3 x + 11$

18.

$6 - 2 x = 10$

19.

$6 x + 3 = x + 18$

20.

$3 x - 10 = 2 x + 12$

21.

$12 x + 3 y = 15$

22.

$x (B + 7) = 9$