Solve for s. |s| + 2 ≥ 18 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value expression: First, we need to isolate the absolute value expression on one side of the inequality. |s| + 2 ≥ 18 Subtract 2 from both sides to isolate |s|. |s| + 2 - 2 ≥ 18 - 2 |s| ≥ 16Set up two inequalities: Now that we have |s| on its own, we can set up two separate inequalities to solve for s because the absolute value of s can be either positive or negative. The two inequalities are: s ≥ 16 and -s ≥ 16Solve second inequality: To solve the second inequality, -s ≥ 16, we need to multiply both sides by -1. Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality sign. -s ≥ 16 (-1)(-s) ≤ (-1)(16) s ≤ -16Final compound inequality: Now we have two inequalities that represent the solution to the original problem: s ≥ 16 or s ≤ -16 This is the compound inequality that represents all the possible values of s that satisfy the original inequality.

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Solve for $s$ . $\newline$ $|s| + 2 \geq 18$

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Algebra 1

Solve absolute value inequalities

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Q. Solve for

s

\newline

|s| + 2 \geq 18

Isolate absolute value expression: First, we need to isolate the absolute value expression on one side of the inequality. $\newline$ $|s| + 2 \geq 18$ $\newline$ Subtract $2$ from both sides to isolate $|s|$ . $\newline$ $|s| + 2 - 2 \geq 18 - 2$ $\newline$ $|s| \geq 16$
Set up two inequalities: Now that we have $\lvert s \rvert$ on its own, we can set up two separate inequalities to solve for $s$ because the absolute value of $s$ can be either positive or negative. $\newline$ The two inequalities are: $\newline$ $s \geq 16$ and $-s \geq 16$
Solve second inequality: To solve the second inequality, $-s \geq 16$ , we need to multiply both sides by $-1$ . Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality sign. $\newline$ $-s \geq 16$ $\newline$ $(-1)(-s) \leq (-1)(16)$ $\newline$ $s \leq -16$
Final compound inequality: Now we have two inequalities that represent the solution to the original problem: $\newline$ $s \geq 16$ or $s \leq -16$ $\newline$ This is the compound inequality that represents all the possible values of $s$ that satisfy the original inequality.