Question

Solve the linear equation $3\left[-14+2\left(15k-6\right)\right]=8\left(3-5k\right)-24$.

Short answer

The solution is$k=\frac{3}{5}$.

Step-by-step solution

Step 1. Given information.

The given equation is$3\left[-14+2\left(15k-6\right)\right]=8\left(3-5k\right)-24$.

Step 2. Simplify inner most parenthesis first

$$\begin{gathered} 3\left[-14+2\left(15k-6\right)\right]=8\left(3-5k\right)-24 \\ 3\left[-14+30k-12\right]=8\left(3-5k\right)-24 \end{gathered}$$

Combine like terms in the braces.

$3\left[30k-26\right]=8\left(3-5k\right)-24$

Step 3. Apply the distributive property to simplify the equation.

Simplify each side of the equation.

$$\begin{gathered} 3\times 30k-3\times 26=8\times 3-8\times 5k-24 \\ 90k-78=24-40k-24 \\ 90k-78=-40k \end{gathered}$$

Step 4. Collect all variables terms on other side of the equation.

Add $40k$to each side.

$$\begin{gathered} 90k-78+40k=-40k+40k \\ 130k-78=0 \end{gathered}$$

Step 5. Collect all constant terms on other side of the equation and then simplify.

Add $78$to each side.

$$\begin{gathered} 130k-78+78=0+78 \\ 130k=78 \end{gathered}$$

Divide each side by $130$.

$$\begin{gathered} \frac{130k}{130}=\frac{78}{130} \\ k=\frac{3}{5} \end{gathered}$$

Hence, the required solution of the given equation is$k=\frac{3}{5}$.