Solve for s. |s| - 3 ≤ 11 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value: We have the inequality |s| - 3 ≤ 11. First, we need to isolate the absolute value term |s| on one side of the inequality. |s| - 3 + 3 ≤ 11 + 3 |s| ≤ 14Interpret absolute value inequality: Now that we have isolated |s|, we can interpret the absolute value inequality. The inequality |s| ≤ 14 means that s is within a distance of 14 from 0 on the number line. This gives us two inequalities: s ≤ 14 and -s ≤ 14Multiply by -1: The second inequality, -s ≤ 14, can be multiplied by -1 to get s ≥ -14. Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign. s ≥ -14Combine inequalities: Combining the two inequalities from the previous steps, we get a compound inequality that represents the solution for s: -14 ≤ s ≤ 14

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Solve for $s$ . $\newline$ $|s| - 3 \leq 11$ $\newline$ 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

s

\newline

|s| - 3 \leq 11

\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: We have the inequality $|s| - 3 \leq 11$ . First, we need to isolate the absolute value term $|s|$ on one side of the inequality. $\newline$ $|s| - 3 + 3 \leq 11 + 3$ $\newline$ $|s| \leq 14$
Interpret absolute value inequality: Now that we have isolated $\lvert s \rvert$ , we can interpret the absolute value inequality. The inequality $\lvert s \rvert \leq 14$ means that $s$ is within a distance of $14$ from $0$ on the number line. $\newline$ This gives us two inequalities: $\newline$ $s \leq 14$ and $-s \leq 14$
Multiply by $-1$ : The second inequality, $-s \leq 14$ , can be multiplied by $-1$ to get $s \geq -14$ . Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign. $\newline$ $s \geq -14$
Combine inequalities: Combining the two inequalities from the previous steps, we get a compound inequality that represents the solution for $s$ : $-14 \leq s \leq 14$