Question

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Answer 1

The answer is D. m≥0.

First the inequality must be simplified.

5(-4m-4)-8(3m+7)≤-76

5*-4m=-20m

5*-4=-20

-8*3m=-24m

-8*7=-56

-20m-20-24m-56≤-76

Now the like terms must be combined.

-20m+-24m=-44m

-20+-56=-76

-44m-76≤-76

Add positive 76 to both sides of the inequality.

-44m-76+76≤-76+76

-44m≤0

Divide both sides by -44.

$\frac{-44m}{-44}$≤$\frac{0}{-44}$

m≥0

(When dividing with a negative number in inequalities, the sign has to be flipped.)

Answer 2

5(-4m - 4) - 8(3m + 7) ≤ -76

Distribute 5 and -8 inside their respective parentheses.

-20m - 20 - 24m - 56 ≤ -76

Combine like terms.

-44m - 76 ≤ -76

Add 76 to both sides.

-44m ≤ 0

Divide both sides by -44 and flip the inequality sign because you are dividing by a negative number.

m ≥ 0

D) m ≥ 0