Question

solve and graph. provide answers accurate to the nearest tenth. |4x - 7| < 9 solution graph number line options skill code: 316027

Explanation:

Step1: Rewrite absolute - value inequality

If \(|a|\lt b\) (\(b > 0\)), then \(-b\lt a\lt b\). So for \(|4x - 7|\lt9\), we have \(-9\lt4x - 7\lt9\).

Step2: Add 7 to all parts

Adding 7 to each part of the compound - inequality \(-9\lt4x - 7\lt9\) gives \(-9 + 7\lt4x-7 + 7\lt9 + 7\), which simplifies to \(-2\lt4x\lt16\).

Step3: Divide by 4

Dividing each part of \(-2\lt4x\lt16\) by 4, we get \(\frac{-2}{4}\lt\frac{4x}{4}\lt\frac{16}{4}\), or \(-0.5\lt x\lt4\).

Answer:

\(-0.5\lt x\lt4\)

To graph:

1. Draw a number line.
2. Mark the points \(x=-0.5\) and \(x = 4\) with open circles (because the inequality is strict, i.e., \(\lt\) not \(\leq\)).
3. Shade the region between the two open - circles.