Question

solve the compound inequality.
4x - 4 ≥ -8 and 2x - 3 < 3
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality \(4x - 4\geq - 8\)

Add \(4\) to both sides:
\(4x-4 + 4\geq - 8+4\)
\(4x\geq - 4\)
Divide both sides by \(4\):
\(x\geq - 1\)

Step2: Solve the second inequality \(2x - 3\lt3\)

Add \(3\) to both sides:
\(2x-3 + 3\lt3 + 3\)
\(2x\lt6\)
Divide both sides by \(2\):
\(x\lt3\)

Step3: Find the intersection of the solutions

Since \(x\geq - 1\) and \(x\lt3\), the solution of the compound - inequality is \(-1\leq x\lt3\)

Answer:

The solution of the compound inequality is \(-1\leq x\lt3\). On the number - line, we draw a closed circle at \(x = - 1\) (because \(x=-1\) is included in the solution set, due to the \(\geq\) sign) and an open circle at \(x = 3\) (because \(x = 3\) is not included in the solution set, due to the \(\lt\) sign), and then connect the two points with a line segment.