Question

algebra 1
homeworkkkkkkkk!!!!!!!!
solve each equation.

1. $|-2n - 2| = 2$
2. $|4 + 2x| = 8$
3. $|4 - n| = 2$
4. $|-x + 2| = 6$
5. $|-p + 4| = 6$
6. $|2x + 4| = 2$

name _________________________ id: 1
date __________ period __

Explanation:

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1) $|-2n - 2| = 2$

Step1: Split absolute value equation

$-2n - 2 = 2 \quad \text{or} \quad -2n - 2 = -2$

Step2: Solve first equation

$-2n = 2 + 2 \\
-2n = 4 \\
n = \frac{4}{-2} = -2$

Step3: Solve second equation

$-2n = -2 + 2 \\
-2n = 0 \\
n = \frac{0}{-2} = 0$

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2) $|4 + 2x| = 8$

Step1: Split absolute value equation

$4 + 2x = 8 \quad \text{or} \quad 4 + 2x = -8$

Step2: Solve first equation

$2x = 8 - 4 \\
2x = 4 \\
x = \frac{4}{2} = 2$

Step3: Solve second equation

$2x = -8 - 4 \\
2x = -12 \\
x = \frac{-12}{2} = -6$

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3) $|4 - n| = 2$

Step1: Split absolute value equation

$4 - n = 2 \quad \text{or} \quad 4 - n = -2$

Step2: Solve first equation

$-n = 2 - 4 \\
-n = -2 \\
n = 2$

Step3: Solve second equation

$-n = -2 - 4 \\
-n = -6 \\
n = 6$

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4) $|-x + 2| = 6$

Step1: Split absolute value equation

$-x + 2 = 6 \quad \text{or} \quad -x + 2 = -6$

Step2: Solve first equation

$-x = 6 - 2 \\
-x = 4 \\
x = -4$

Step3: Solve second equation

$-x = -6 - 2 \\
-x = -8 \\
x = 8$

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5) $|-p + 4| = 6$

Step1: Split absolute value equation

$-p + 4 = 6 \quad \text{or} \quad -p + 4 = -6$

Step2: Solve first equation

$-p = 6 - 4 \\
-p = 2 \\
p = -2$

Step3: Solve second equation

$-p = -6 - 4 \\
-p = -10 \\
p = 10$

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6) $|2x + 4| = 2$

Step1: Split absolute value equation

$2x + 4 = 2 \quad \text{or} \quad 2x + 4 = -2$

Step2: Solve first equation

$2x = 2 - 4 \\
2x = -2 \\
x = \frac{-2}{2} = -1$

Step3: Solve second equation

$2x = -2 - 4 \\
2x = -6 \\
x = \frac{-6}{2} = -3$

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Answer:

1. $n = -2$ or $n = 0$
2. $x = 2$ or $x = -6$
3. $n = 2$ or $n = 6$
4. $x = -4$ or $x = 8$
5. $p = -2$ or $p = 10$
6. $x = -1$ or $x = -3$