Question

solve the inequality and graph the solution set on a number line.
-36 < 7x - 1 ≤ -29
what is the solution set?
{x | -5 < x ≤ -4} (type an inequality.)
choose the correct graph below.

Explanation:

Step1: Solve the left - hand side of the compound inequality

We have \(-36<7x - 1\).
Add \(1\) to all parts of the inequality: \(-36 + 1<7x-1 + 1\), which simplifies to \(-35<7x\).
Divide by \(7\): \(\frac{-35}{7}<\frac{7x}{7}\), so \(-5 < x\).

Step2: Solve the right - hand side of the compound inequality

We have \(7x-1\leq - 29\).
Add \(1\) to all parts of the inequality: \(7x-1 + 1\leq-29 + 1\), which simplifies to \(7x\leq-28\).
Divide by \(7\): \(\frac{7x}{7}\leq\frac{-28}{7}\), so \(x\leq - 4\).

Answer:

The solution set is \(\{x|-5 < x\leq - 4\}\).

For the graph:

• Option D has an open circle at \(-5\) (because \(x>-5\), not including \(-5\)) and a closed circle at \(-4\) (because \(x\leq - 4\), including \(-4\)) with a line segment connecting them. So the correct graph is D.