Solve for w. -2|w| ≤ -12 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Divide and Reverse Inequality: We have the inequality: -2|w| ≤ -12 First, we divide both sides by -2 to isolate |w|. Remember that dividing by a negative number reverses the inequality sign. -2|w| / -2 ≥ -12 / -2 |w| ≥ 6 Interpret Absolute Value Inequality: Now we interpret the absolute value inequality |w| ≥ 6. This means that w is either greater than or equal to 6 or less than or equal to -6. So we have two inequalities: w ≥ 6 or w ≤ -6Write Compound Inequality: We can write this as a compound inequality: w ≤ -6 or w ≥ 6 This is the final answer in the form of a compound inequality.

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Solve for $w$ . $\newline$ $-2|w| \leq -12$ $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form. $\newline$ ______

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Algebra 1

Solve absolute value inequalities

Full solution

Q. Solve for

w

\newline

-2|w| \leq -12

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

______

Divide and Reverse Inequality: We have the inequality: $\newline$ $-2|w| \leq -12$ $\newline$ First, we divide both sides by $-2$ to isolate $|w|$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $-2|w| / -2 \geq -12 / -2$ $\newline$ $|w| \geq 6$
Interpret Absolute Value Inequality: Now we interpret the absolute value inequality $|w| \geq 6$ . This means that $w$ is either greater than or equal to $6$ or less than or equal to $-6$ . So we have two inequalities: $w \geq 6$ or $w \leq -6$
Write Compound Inequality: We can write this as a compound inequality: $\newline$ $w \leq -6$ or $w \geq 6$ $\newline$ This is the final answer in the form of a compound inequality.