Solve for s. |-2s| ≥ 8 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Identify Inequality: We have the inequality: |-2s| ≥ 8 First, we solve for |-2s|. |-2s| ≥ 8 This means that -2s is either greater than or equal to 8 or less than or equal to -8, because the absolute value of a number is the distance from zero, which is always non-negative.Split into Two: Now we split the inequality into two separate inequalities to remove the absolute value: -2s ≥ 8 or -2s ≤ -8Solve First Inequality: We solve the first inequality: -2s ≥ 8 Divide both sides by -2, remembering to flip the inequality sign because we are dividing by a negative number: s ≤ -4Solve Second Inequality: We solve the second inequality: -2s ≤ -8 Divide both sides by -2, again flipping the inequality sign: s ≥ 4Combine Inequalities: Now we combine both inequalities into a compound inequality: s ≤ -4 or s ≥ 4 This is the solution to the original problem.

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Solve for $s$ . $\newline$ $|-2s| \geq 8$ $\newline$ 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 2

Solve absolute value inequalities

Full solution

Q. Solve for

s

\newline

|-2s| \geq 8

\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

______

Identify Inequality: We have the inequality: $\newline$ $|-2s| \geq 8$ $\newline$ First, we solve for $|-2s|$ . $\newline$ $|-2s| \geq 8$ $\newline$ This means that $-2s$ is either greater than or equal to $8$ or less than or equal to $-8$ , because the absolute value of a number is the distance from zero, which is always non-negative.
Split into Two: Now we split the inequality into two separate inequalities to remove the absolute value: $-2s \geq 8$ or $-2s \leq -8$
Solve First Inequality: We solve the first inequality: $\newline$ $-2s \geq 8$ $\newline$ Divide both sides by $-2$ , remembering to flip the inequality sign because we are dividing by a negative number: $\newline$ $s \leq -4$
Solve Second Inequality: We solve the second inequality: $\newline$ $-2s \leq -8$ $\newline$ Divide both sides by $-2$ , again flipping the inequality sign: $\newline$ $s \geq 4$
Combine Inequalities: Now we combine both inequalities into a compound inequality: $s \leq -4$ or $s \geq 4$ This is the solution to the original problem.