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

Isolate absolute value term: We have the inequality: -|s| ≤ -3 First, we need to isolate the absolute value term |s|. To do this, we multiply both sides of the inequality by -1, remembering that this reverses the inequality sign. -1 * (-|s|) ≥ -1 * (-3) |s| ≥ 3Break into two inequalities: Now that we have |s| ≥ 3, we can break this into two separate inequalities because the absolute value of s can be either positive or negative. s ≥ 3 or -s ≥ 3Rewrite second inequality: The second inequality, -s ≥ 3, can be rewritten by multiplying both sides by -1, which again reverses the inequality sign. -s ≥ 3 s ≤ -3Final compound inequality: We now have two inequalities that represent the solution to the original problem: s ≥ 3 or s ≤ -3 This is the compound inequality that represents all the possible values of s that satisfy the original inequality.

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Solve for $s$ . $\newline$ $-|s| \leq -3$ $\newline$ $\newline$ 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

-|s| \leq -3

\newline

\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

______

Isolate absolute value term: We have the inequality: $\newline$ $-|s| \leq -3$ $\newline$ First, we need to isolate the absolute value term $|s|$ . To do this, we multiply both sides of the inequality by $-1$ , remembering that this reverses the inequality sign. $\newline$ $-1 \cdot (-|s|) \geq -1 \cdot (-3)$ $\newline$ $|s| \geq 3$
Break into two inequalities: Now that we have $|s| \geq 3$ , we can break this into two separate inequalities because the absolute value of $s$ can be either positive or negative. $s \geq 3$ or $-s \geq 3$
Rewrite second inequality: The second inequality, $-s \geq 3$ , can be rewritten by multiplying both sides by $-1$ , which again reverses the inequality sign. $\newline$ $-s \geq 3$ $\newline$ $s \leq -3$
Final compound inequality: We now have two inequalities that represent the solution to the original problem: $\newline$ $s \geq 3$ or $s \leq -3$ $\newline$ This is the compound inequality that represents all the possible values of $s$ that satisfy the original inequality.