Question

which graph represents the solutions to this inequality? 3b + 7 < 16 or 5b + 2 > 37

Explanation:

Step1: Solve the first inequality

Solve \(3b + 7<16\). Subtract 7 from both sides: \(3b<16 - 7\), so \(3b<9\). Then divide both sides by 3, we get \(b < 3\).

Step2: Solve the second inequality

Solve \(5b+2>37\). Subtract 2 from both sides: \(5b>37 - 2\), so \(5b>35\). Then divide both sides by 5, we get \(b>7\).

Step3: Analyze the solution set

The solution of the compound - inequality \(3b + 7<16\) or \(5b + 2>37\) is \(b < 3\) or \(b>7\). On a number - line, this is represented by an open circle at 3 with an arrow pointing to the left and an open circle at 7 with an arrow pointing to the right.

Answer:

The graph with open circles at 3 and 7 and arrows pointing in opposite directions (left from 3 and right from 7) represents the solution.