Question

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question 39 practice similar questions
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solve: $-12 < 4x + 3 \leq 12$
state your solution as a compound inequality.
use fractions in simplest forms (for example $-\frac{1}{2} < x \leq \frac{1}{2}$):
enter your answer

Explanation:

Step1: Subtract 3 from all parts

To isolate the term with \( x \), we subtract 3 from each part of the compound inequality. So we have \(-12 - 3 < 4x + 3 - 3 \leq 12 - 3\), which simplifies to \(-15 < 4x \leq 9\).

Step2: Divide all parts by 4

To solve for \( x \), we divide each part of the inequality by 4. This gives \(\frac{-15}{4} < \frac{4x}{4} \leq \frac{9}{4}\), which simplifies to \(-\frac{15}{4} < x \leq \frac{9}{4}\).

Answer:

\(-\frac{15}{4} < x \leq \frac{9}{4}\)