Question

Which of the following are solutions to the inequality below? Select all that apply.

–6u ≥ 34

u= 9
u= 4
u= -8
u= 2

Answer 1

To solve the inequality \( -6u \geq 34 \), we first divide both sides by -6. Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign.

\[
u \leq -\frac{34}{6}
\]

Simplifying \( -\frac{34}{6} \):

\[
-\frac{34}{6} = -\frac{17}{3} \approx -5.67
\]

So the inequality becomes:

\[
u \leq -\frac{17}{3}
\]

Now we will check each candidate solution to see if it satisfies the inequality \( u \leq -\frac{17}{3} \):

1. **For \( u = 9 \)**:
\( 9 \) is not less than or equal to \( -5.67 \). **Not a solution.**

2. **For \( u = 4 \)**:
\( 4 \) is not less than or equal to \( -5.67 \). **Not a solution.**

3. **For \( u = -8 \)**:
\( -8 \) is less than \( -5.67 \). **Is a solution.**

4. **For \( u = 2 \)**:
\( 2 \) is not less than or equal to \( -5.67 \). **Not a solution.**

The only solution to the inequality \( -6u \geq 34 \) is:

**u = -8**.