Question

Solve the linear equation$-12+8\left(x-5\right)=-4+3\left(5x-2\right)$.

Short answer

The solution is$x=-6$.

Step-by-step solution

Step 1. Given information.

The given equation is$-12+8\left(x-5\right)=-4+3\left(5x-2\right)$.

Step 2. Apply the distributive property to simplify the equation.

Simplify each side of the equation.

$$\begin{gathered} -12+8x-8\times 5=-4+3\times 5x-3\times 2 \\ -12+8x-40=-4+15x-6 \\ 8x-52=15x-10 \end{gathered}$$

Step 3. Collect all variables terms on other side of the equation.

Subtract $15x$from each side.

$$\begin{gathered} 8x-52-15x=15x-10-15x \\ -7x-52=-10 \end{gathered}$$

Step 4. Collect all constant terms on other side of the equation and then simplify.

Add $52$to each side.

$$\begin{gathered} -7x-52+52=-10+52 \\ -7x=42 \end{gathered}$$

Divide each side by$-7$.

$$\begin{gathered} \frac{-7x}{-7}=\frac{42}{-7} \\ x=-6 \end{gathered}$$

Hence, the solution of the given linear equation is$x=-6$.