Question

graph the solution to the inequality on the number line. |4y + 6| < 10

Explanation:

Step1: Remove absolute - value

We know that if \(|a|\lt b\) (\(b > 0\)), then \(-b\lt a\lt b\). So for \(|4y + 6|\lt10\), we have \(- 10\lt4y + 6\lt10\).

Step2: Subtract 6 from all parts

\(-10-6\lt4y+6 - 6\lt10 - 6\), which simplifies to \(-16\lt4y\lt4\).

Step3: Divide all parts by 4

\(\frac{-16}{4}\lt\frac{4y}{4}\lt\frac{4}{4}\), resulting in \(-4\lt y\lt1\).

Step4: Graph on number - line

On the number - line, we use open circles at \(y=-4\) and \(y = 1\) (because the inequality is strict, i.e., \(\lt\) not \(\leq\)) and shade the region between them.

Answer:

On the number - line, place open circles at \(-4\) and \(1\) and shade the region between them.