Question

solve for q and graph the solution. 5|q + 29| > 10 click two endpoints to graph a line segment, an endpoint and a ray, or two arrowheads to graph a line. to change endpoints from filled circles, click on them. -33 -32 -31 -30 -29 -28 -27 -26 -25 -24

Explanation:

Step1: Divide both sides by 5

To isolate the absolute value expression, we divide both sides of the inequality \(5|q + 29|>10\) by 5. This gives us \(|q + 29|>\frac{10}{5}\), which simplifies to \(|q + 29|>2\).

Step2: Solve the absolute value inequality

The absolute value inequality \(|x|>a\) (where \(a>0\)) is equivalent to \(x > a\) or \(x < -a\). Applying this to \(|q + 29|>2\), we get two separate inequalities:

1. \(q + 29>2\)
2. \(q + 29 < - 2\)

For the first inequality \(q + 29>2\), we subtract 29 from both sides: \(q>2 - 29\), so \(q>-27\).

For the second inequality \(q + 29 < - 2\), we subtract 29 from both sides: \(q < - 2-29\), so \(q < - 31\).

Answer:

The solution to the inequality is \(q < - 31\) or \(q>-27\). To graph this, we would have two rays: one starting at \(-31\) (with an open circle, since the inequality is strict) and extending to the left, and another starting at \(-27\) (with an open circle) and extending to the right.