Solve for w. |-2w| > 14 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Given Inequality: We have the inequality: |-2w| > 14 First, we need to solve for |2w|. |-2w| > 14 This means that the absolute value of -2w is greater than 14.Split into Two Cases: The absolute value inequality |-2w| > 14 can be split into two separate inequalities because if the absolute value of a number is greater than 14, the number itself can either be greater than 14 or less than -14. So we have two cases: -2w > 14 or -2w 14 To isolate w, we divide both sides by -2. Remember that dividing by a negative number reverses the inequality sign. w 7Combine Inequalities: Combining both inequalities, we get the compound inequality: w 7 This is the solution to the original problem.

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Solve for $w$ . $\newline$ |-2w| > 14 $\newline$ 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

|-2w| > 14

\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

______

Given Inequality: We have the inequality: $\newline$ |-2w| > 14 $\newline$ First, we need to solve for $|2w|$ . $\newline$ |-2w| > 14 $\newline$ This means that the absolute value of $-2w$ is greater than $14$ .
Split into Two Cases: The absolute value inequality |-2w| > 14 can be split into two separate inequalities because if the absolute value of a number is greater than $14$ , the number itself can either be greater than $14$ or less than $-14$ . $\newline$ So we have two cases: $\newline$ -2w > 14 or -2w < -14
Solve First Inequality: Let's solve the first inequality: $\newline$ -2w > 14 $\newline$ To isolate $w$ , we divide both sides by $-2$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ w < -7
Solve Second Inequality: Now let's solve the second inequality: $\newline$ -2w < -14 $\newline$ Again, we divide both sides by $-2$ , and the inequality sign reverses. $\newline$ w > 7
Combine Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ w < -7 or w > 7 $\newline$ This is the solution to the original problem.