Question

solve the compound inequality.

3x + 5 ≥ -1 or 2x + 3 > 13

graph the solution on the number line.
if there is no solution, click on
o solution\.

Explanation:

Step1: Solve \(3x + 5\geq - 1\)

Subtract \(5\) from both sides: \(3x\geq -1 - 5\), so \(3x\geq -6\).
Divide both sides by \(3\): \(x\geq - 2\).

Step2: Solve \(2x+3>13\)

Subtract \(3\) from both sides: \(2x>13 - 3\), so \(2x>10\).
Divide both sides by \(2\): \(x > 5\).

Since it is an "or" compound inequality, the solution is \(x\geq - 2\) or \(x>5\). The more inclusive solution is \(x\geq - 2\) (because all values of \(x>5\) are already included in \(x\geq - 2\)).

To graph \(x\geq - 2\) on the number - line:

• Place a closed circle at \(x = - 2\) (because the inequality is \(\geq\), so \(-2\) is included in the solution set).
• Shade to the right of \(x=-2\).

Answer:

The solution of the compound inequality \(3x + 5\geq - 1\) or \(2x + 3>13\) is \(x\geq - 2\). On the number - line, place a closed circle at \(-2\) and shade to the right.