Question

Solve each equation. Check your solutions.

$3(2k-2)=-2(4k-11)$

Short answer

The$k=2$ is the solution of the given equation.

Step-by-step solution

Step 1. Given information.

We have an equation $3(2k-2)=-2(4k-11)$.

To find the solution of the given equation and check the solution.

Step 2. Calculation.

Solving the given equation:

$\begin{array}{l}3(2k-2)=-2(4k-11)\\ \Rightarrow 6k-6=-8k+22\\ \Rightarrow 6k+8k=6+22\\ \Rightarrow 14k=28\\ \Rightarrow k=2\end{array}$

Step 3. Check the Solution.

We substitute the$k=2$ in the given equation.

$\begin{array}{l}3(2k-2)=-2(4k-11)\\ \Rightarrow 3(2\times 2-2)=-2(4\times 2-11)\\ \Rightarrow 3(4-2)=-2(8-11)\\ \Rightarrow 3\left(2\right)=-2(-3)\\ \Rightarrow 6=6\\ \Rightarrow L.H.S.=R.H.S.\end{array}$

Hence, the$k=2$ is the solution of the given equation.