Question

solve the compound inequality.
2x + 6 ≥ 4 and 3x + 4 ≤ 13
graph the solution on the number line.

Explanation:

Step1: Solve \(2x + 6\geq4\)

Subtract 6 from both sides:
\(2x+6 - 6\geq4 - 6\)
\(2x\geq - 2\)
Divide both sides by 2:
\(x\geq - 1\)

Step2: Solve \(3x + 4\leq13\)

Subtract 4 from both sides:
\(3x+4 - 4\leq13 - 4\)
\(3x\leq9\)
Divide both sides by 3:
\(x\leq3\)

Answer:

The solution of the compound inequality is \(-1\leq x\leq3\). On the number - line, we draw a solid circle at \(x = - 1\) (because \(x=-1\) is included in the solution, since the inequality is \(\geq\)) and a solid circle at \(x = 3\) (because \(x = 3\) is included in the solution, since the inequality is \(\leq\)), and then connect the two points with a line segment.