Lesson 6 Taking Sides Practice Understanding

Ready

Graph each set of equations and find the point where they intersect.

1.

$y = - \frac{1}{3} x + 4$

$y = - x + 2$

Point:

2.

$y = x + 3$

$y = - 2 x - 3$

Point:

3.

$y = - \frac{1}{2} x - 3$

$y = \frac{1}{4} x + 3$

Point:

4.

$y = - x - 2$

$y = 2 x - 8$

Point:

Set

Each inequality below was solved incorrectly. Identify the mistakes that were made. Then, correct the mistakes and provide the correct solution.

5.

$3 x - 2 \leq 2 x + 5$

$\begin{aligned} 3 x - 2 & \leq 2 x + 5 \\ + 2 & + 2 \\ 3 x & \leq 4 x + 5 \\ - 5 & - 5 \\ 3 x - 5 & \leq 4 x \\ - 3 x & - 3 x \\ - 5 & \leq x \end{aligned}$

6.

$16 - 3 x > - 5 x + 4$

$\begin{aligned} 16 - 3 x & > - 5 x + 4 \\ + 3 x & + 3 x \\ \frac{16}{- 2} & > \frac{- 2 x}{- 2} \\ - 8 & < x \end{aligned}$

7.

$- 2 (x + 7) + 3 \geq 25$

$\begin{aligned} - 2 (x + 7) + 3 & \geq 25 \\ - 3 & - 3 \\ - 2 (x + 7) & \geq 22 \\ - 2 x - 14 & \leq 22 \\ + 14 & + 14 \\ \frac{- 2 x}{- 2} & \leq \frac{36}{- 2} \\ x & \geq - 18 \end{aligned}$

8.

$- 54 - 7 x < 5 x + 6$

$\begin{aligned} - 54 - 7 x & < 5 x + 6 \\ - 6 & - 6 \\ - 60 - 7 x & > 5 x \\ + 7 x & + 7 x \\ \frac{- 60}{12} & > \frac{12 x}{12} \\ - 5 & > x \end{aligned}$

Solve each inequality.

9.

$4 x + 3 < - 1$

10.

$4 - 6 x \leq 2 (2 x + 3)$

11.

$6 (4 x + 3) \geq 2 (x - 2)$

12.

$24 > - 5 x - 6$

Go

Solve each literal equation for the indicated variable.

13.

The area formula of a regular polygon is $A = \frac{1}{2} P a$ . The variable $a$ represents the apothem and $P$ represents the perimeter of the polygon. Solve the equation for the apothem, $a$ .

14.

The equation $y = m x + b$ is the equation of a line. Solve the equation for $b$ .

15.

The equation for the circumference, $c$ , of a circle with radius $r$ is $c = 2 π r$ . Solve the equation for the radius, $r$ .

16.

The equation for the area of a circle, $A$ , based on diameter, $d$ , is $A = π \frac{d^{2}}{4}$ . Solve the equation to isolate the diameter, $d$ .