Question

solve for q and graph the solution. -35 < -7|q + 95| click two endpoints to graph a line segment, an endpoint and an arrow ray, or two arrowheads to graph a line. to change endpoints from filled - in circles, click on them. -100 -95 -90 -85 -80 -75 -70 -65 -60 -55 -50

Explanation:

Step1: Divide both sides by -7 (reverse inequality)

When dividing an inequality by a negative number, the inequality sign flips. So, divide both sides of \(-35 < -7|q + 95|\) by \(-7\):
\(\frac{-35}{-7} > |q + 95|\)
Simplify \(\frac{-35}{-7}\) to get \(5 > |q + 95|\).

Step2: Rewrite absolute value inequality

The inequality \(|x| < a\) (where \(a>0\)) is equivalent to \(-a < x < a\). Here, \(x = q + 95\) and \(a = 5\), so we rewrite \(5 > |q + 95|\) as:
\(-5 < q + 95 < 5\)

Step3: Solve left inequality

Subtract 95 from all parts. First, solve \(-5 < q + 95\):
Subtract 95 from both sides: \(-5 - 95 < q\)
Simplify \(-5 - 95\) to get \(-100 < q\).

Step4: Solve right inequality

Solve \(q + 95 < 5\):
Subtract 95 from both sides: \(q < 5 - 95\)
Simplify \(5 - 95\) to get \(q < -90\).

Step5: Combine inequalities

From Step3 and Step4, we have \(-100 < q < -90\).

Answer:

The solution for \(q\) is \(-100 < q < -90\). To graph this, we use an open circle at \(-100\) and an open circle at \(-90\) with a line segment connecting them (since the endpoints are not included, we use open circles).