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

Understand absolute value inequality: First, let's understand the absolute value inequality. The inequality |-w| ≤ 12 means that the absolute value of -w is less than or equal to 12. This implies that -w must be within the range of -12 to 12, including the endpoints.Write compound inequality: Now, let's write the compound inequality based on the definition of absolute value. The absolute value of a number is less than or equal to 12 if the number itself is greater than or equal to -12 and less than or equal to 12. Therefore, we have -12 ≤ -w ≤ 12.Solve for w: Next, we need to solve for w. To do this, we can multiply the entire inequality by -1 to get rid of the negative sign in front of w. Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality signs. So, multiplying by -1 gives us 12 ≥ w ≥ -12.Final compound inequality: Finally, we can write the compound inequality in the correct order, from the smallest to the largest value that w can take. The final compound inequality is -12 ≤ w ≤ 12.

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Solve for $w$ . $\newline$ $|-w| \leq 12$ $\newline$ 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

|-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

______

Understand absolute value inequality: First, let's understand the absolute value inequality. The inequality $|-w| \leq 12$ means that the absolute value of $-w$ is less than or equal to $12$ . This implies that $-w$ must be within the range of $-12$ to $12$ , including the endpoints.
Write compound inequality: Now, let's write the compound inequality based on the definition of absolute value. The absolute value of a number is less than or equal to $12$ if the number itself is greater than or equal to $-12$ and less than or equal to $12$ . Therefore, we have $-12 \leq -w \leq 12$ .
Solve for $w$ : Next, we need to solve for $w$ . To do this, we can multiply the entire inequality by $-1$ to get rid of the negative sign in front of $w$ . Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality signs. So, multiplying by $-1$ gives us $12 \geq w \geq -12$ .
Final compound inequality: Finally, we can write the compound inequality in the correct order, from the smallest to the largest value that $w$ can take. The final compound inequality is $-12 \leq w \leq 12$ .