Question

which graph represents the solutions to this inequality? -2u - 33 < -47 and -6u + 11 > -67

Explanation:

Step1: Solve the first inequality

Solve \(-2u - 33\lt - 47\). Add 33 to both sides: \(-2u-33 + 33\lt-47 + 33\), which simplifies to \(-2u\lt - 14\). Divide both sides by - 2 and reverse the inequality sign (since dividing by a negative number), we get \(u > 7\).

Step2: Solve the second inequality

Solve \(-6u + 11>-67\). Subtract 11 from both sides: \(-6u+11 - 11>-67 - 11\), which simplifies to \(-6u>-78\). Divide both sides by - 6 and reverse the inequality sign, we get \(u < 13\).

Step3: Determine the solution set

The solution of the compound - inequality is \(7 < u < 13\). This is represented by a number line with open circles at 7 and 13 and a line segment between them.

Answer:

The third graph (the one with open - circles at 7 and 13 and a line segment between them)