Solve for s. |s| + 3 ≤ 4 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 ≤ 4. The first step is to isolate the absolute value term |s| by subtracting 3 from both sides of the inequality. |s| + 3 - 3 ≤ 4 - 3 |s| ≤ 1Consider absolute value definition: Now that we have |s| ≤ 1, we need to consider the definition of absolute value. The absolute value of a number is the distance from zero on the number line, so |s| ≤ 1 means that s is within 1 unit of zero. This gives us two inequalities: s ≤ 1 and -s ≤ 1 (which is equivalent to s ≥ -1).Combine inequalities: Combining the two inequalities from the previous step, we get the compound inequality: -1 ≤ s ≤ 1 This inequality represents all the values of s that are within 1 unit of zero on the number line.

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Solve for $s$ . $\newline$ $|s| + 3 \leq 4$ $\newline$ 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

|s| + 3 \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 term: We have the inequality $|s| + 3 \leq 4$ . The first step is to isolate the absolute value term $|s|$ by subtracting $3$ from both sides of the inequality. $\newline$ $|s| + 3 - 3 \leq 4 - 3$ $\newline$ $|s| \leq 1$
Consider absolute value definition: Now that we have $|s| \leq 1$ , we need to consider the definition of absolute value. The absolute value of a number is the distance from zero on the number line, so $|s| \leq 1$ means that $s$ is within $1$ unit of zero. This gives us two inequalities: $s \leq 1$ and $-s \leq 1$ (which is equivalent to $s \geq -1$ ).
Combine inequalities: Combining the two inequalities from the previous step, we get the compound inequality: $\newline$ $-1 \leq s \leq 1$ $\newline$ This inequality represents all the values of $s$ that are within $1$ unit of zero on the number line.