Question

(\frac{1}{2}(8c + 10) > 4(2c - 6) + 1)

Explanation:

Step1: Simplify both sides

Simplify the left side: $\frac{1}{2}(8c + 10)=4c + 5$.
Simplify the right side: $4(2c - 6)+1 = 8c - 24 + 1 = 8c - 23$.
Now the inequality is $4c + 5 > 8c - 23$.

Step2: Move variables to one side

Subtract $4c$ from both sides: $5 > 4c - 23$.

Step3: Solve for \( c \)

Add 23 to both sides: $28 > 4c$.
Divide both sides by 4: $7 > c$, or $c < 7$.

Answer:

\( c < 7 \)