solve the following inequality for q. write your answer in simplest form.\n3q - (5q + 1) > -5q - 7 - 5q

Explanation:

Step1: Simplify left - hand side

Expand $3q-(5q + 1)$ to get $3q-5q - 1=-2q - 1$.

Step2: Simplify right - hand side

Combine like terms on the right - hand side: $-5q-7 - 5q=-10q-7$.

Step3: Rearrange the inequality

The original inequality $3q-(5q + 1)>-5q-7 - 5q$ becomes $-2q - 1>-10q-7$. Add $10q$ to both sides: $-2q+10q - 1>-10q+10q-7$, which simplifies to $8q - 1>-7$.

Step4: Isolate the variable term

Add 1 to both sides: $8q-1 + 1>-7 + 1$, so $8q>-6$.

Step5: Solve for q

Divide both sides by 8: $q>-\frac{6}{8}=-\frac{3}{4}$.

Answer:

$q>-\frac{3}{4}$