Question

Solve:$8(q+1)-5=3(2q-4)-1$.

Short answer

The solution is$q=-8$.

Step-by-step solution

Step 1. Given information.

Solve the below linear equation,

$8(q+1)-5=3(2q-4)-1$.

Step 2. Use the Distributive Property to remove any parentheses. 

Combine like terms and simplify.

$$\begin{gathered} 8(q+1)-5=3(2q-4)-1 \\ 8·q+8·1-5=3·2q-3·4-1 \\ 8q+8-5=6q-12-1 \\ 8q+3=6q-13 \\ 8q+3-6q=6q-13-6q \\ 2q+3=-13 \\ 2q+3-3=-13-3 \\ 2q=-16 \\ \frac{2q}{2}=\frac{-16}{2} \\ q=-8 \end{gathered}$$

Step 3. Check the solution.

Put $q=-8$into the equation.

$$\begin{gathered} 8(q+1)-5=3(2q-4)-1 \\ 8(-8+1)-5=3(2·(-8)-4)-1 \\ 8(-7)-5=3(-16-4)-1 \\ -56-5=3(-20)-1 \\ -61=-60-1 \\ -61=-61 \end{gathered}$$

Hence, the solution is correct.

Step 4. Conclusion.

The solution of the given linear equation is$q=-8$.