Solve for w. |-7w| ≤ 7 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Absolute Value Inequality: We have the inequality: |-7w| ≤ 7 First, we need to solve for |7w|. |-7w| ≤ 7 This means that the absolute value of -7w is less than or equal to 7.Split into Two Inequalities: The absolute value inequality |-7w| ≤ 7 can be split into two separate inequalities: -7w ≤ 7 and -7w ≥ -7Solve First Inequality: Let's solve the first inequality: -7w ≤ 7 To isolate w, we divide both sides by -7. Remember that dividing by a negative number reverses the inequality sign. w ≥ -1Solve Second Inequality: Now let's solve the second inequality: -7w ≥ -7 Again, we divide both sides by -7, which reverses the inequality sign. w ≤ 1Combine Inequalities: Combining both inequalities, we get the compound inequality: -1 ≤ w ≤ 1 This is the solution to the original absolute value inequality.

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Solve for $w$ . $\newline$ $|-7w| \leq 7$ $\newline$ 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

|-7w| \leq 7

\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

______

Absolute Value Inequality: We have the inequality: $\newline$ $|-7w| \leq 7$ $\newline$ First, we need to solve for $|7w|$ . $\newline$ $|-7w| \leq 7$ $\newline$ This means that the absolute value of $-7w$ is less than or equal to $7$ .
Split into Two Inequalities: The absolute value inequality $|-7w| \leq 7$ can be split into two separate inequalities: $\newline$ $-7w \leq 7$ and $-7w \geq -7$
Solve First Inequality: Let's solve the first inequality: $\newline$ $-7w \leq 7$ $\newline$ To isolate $w$ , we divide both sides by $-7$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $w \geq -1$
Solve Second Inequality: Now let's solve the second inequality: $\newline$ $-7w \geq -7$ $\newline$ Again, we divide both sides by $-7$ , which reverses the inequality sign. $\newline$ $w \leq 1$
Combine Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $-1 \leq w \leq 1$ $\newline$ This is the solution to the original absolute value inequality.