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 \( u \leq -\frac{17}{3} \):
-
For \( u = 9 \):
\( 9 \) is not less than or equal to \( -5.67 \). Not a solution. -
For \( u = 4 \):
\( 4 \) is not less than or equal to \( -5.67 \). Not a solution. -
For \( u = -8 \):
\( -8 \) is less than \( -5.67 \). Is a solution. -
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.
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