Question

midterm review
warm up #1
name
solve the equation.

1. $\frac{x}{4} - 9 = 5$
2. $x - 2(3x - 2) = -6$
3. $5x - 16 = 14 - 5x$
4. $-4(x + 6) + 2x = 3(x + 2)$
5. $-4(x + 4) = -2(2x + 8)$
6. $3x - 6 + 2x = 5(x - 6)$

solve the absolute value equation. (hint: be sure to set up both cases)

1. $|x| - 5 = 6$
2. $|x + 3| = 8$
3. $|x + 2| + 5 = 3$

Explanation:

Problem 1: $\boldsymbol{\frac{x}{4} - 9 = 5}$

Step1: Add 9 to both sides

$\frac{x}{4} - 9 + 9 = 5 + 9$
$\frac{x}{4} = 14$

Step2: Multiply both sides by 4

$\frac{x}{4} \times 4 = 14 \times 4$
$x = 56$

Step1: Distribute -2

$x - 6x + 4 = -6$

Step2: Combine like terms

$-5x + 4 = -6$

Step3: Subtract 4 from both sides

$-5x + 4 - 4 = -6 - 4$
$-5x = -10$

Step4: Divide by -5

$\frac{-5x}{-5} = \frac{-10}{-5}$
$x = 2$

Step1: Add 5x to both sides

$5x + 5x - 16 = 14 - 5x + 5x$
$10x - 16 = 14$

Step2: Add 16 to both sides

$10x - 16 + 16 = 14 + 16$
$10x = 30$

Step3: Divide by 10

$\frac{10x}{10} = \frac{30}{10}$
$x = 3$

Answer:

$x = 56$

Problem 2: $\boldsymbol{x - 2(3x - 2) = -6}$