Question

solve the following inequality.
55m - (m + 4) > - 8(m - 2)

select the correct choice below and fill in the answer box to complete your choice.

a. the solution set is {m|m < }

b. the solution set is {m|m ≥ }

c. the solution set is {m|m > }

d. the solution set is {m|m ≤ }

Explanation:

Step1: Simplify the left - hand side

First, simplify the expression inside the brackets: $5m-(m + 4)=5m - m-4=4m - 4$. Then multiply by 5: $5(4m - 4)=20m-20$.

Step2: Simplify the right - hand side

Expand $-8(m - 2)$ using the distributive property: $-8(m - 2)=-8m + 16$.

Step3: Solve the inequality

The original inequality $5[5m-(m + 4)]>-8(m - 2)$ becomes $20m-20>-8m + 16$. Add $8m$ to both sides: $20m+8m-20>-8m+8m + 16$, which simplifies to $28m-20>16$. Add 20 to both sides: $28m-20 + 20>16+20$, so $28m>36$. Divide both sides by 28: $m>\frac{36}{28}=\frac{9}{7}$.

Answer:

C. The solution set is $\{m|m>\frac{9}{7}\}$