Solve for s. |4s| ≤ 4 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value: We have the inequality |4s| ≤ 4. To solve for s, we first isolate the absolute value expression.Split into two inequalities: Since |4s| represents the absolute value of 4s, we can split the inequality into two separate inequalities without the absolute value: 4s ≤ 4 and -4s ≤ 4.Solve first inequality: Let's solve the first inequality: 4s ≤ 4. We divide both sides by 4 to isolate s. s ≤ 4 / 4 s ≤ 1Solve second inequality: Now, let's solve the second inequality: -4s ≤ 4. We divide both sides by -4. Remember that dividing by a negative number reverses the inequality sign. s ≥ 4 / -4 s ≥ -1Combine both inequalities: Combining both inequalities, we get the compound inequality -1 ≤ s ≤ 1, which represents the solution to the original problem.

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Solve for $s$ . $\newline$ $|4s| \leq 4$ $\newline$ 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

|4s| \leq 4

\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 $|4s| \leq 4$ . To solve for $s$ , we first isolate the absolute value expression.
Split into two inequalities: Since $|4s|$ represents the absolute value of $4s ext{,}$ we can split the inequality into two separate inequalities without the absolute value: $4s \leq 4$ and $-4s \leq 4$ .
Solve first inequality: Let's solve the first inequality: $4s \leq 4$ . We divide both sides by $4$ to isolate $s$ . $\newline$ $s \leq \frac{4}{4}$ $\newline$ $s \leq 1$
Solve second inequality: Now, let's solve the second inequality: $-4s \leq 4$ . We divide both sides by $-4$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $s \geq \frac{4}{-4}$ $\newline$ $s \geq $-1$
Combine both inequalities: Combining both inequalities, we get the compound inequality $-1 \leq s \leq 1$, which represents the solution to the original problem.