Question

Solve each equation. Check your solution.

$6\left(3a+1\right)-30=3\left(2a-4\right)$

Short answer

The solution of the given equation is $a=1$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$6\left(3a+1\right)-30=3\left(2a-4\right)$”.

Step 2. Solve the given equation.

Solving,

$6\left(3a+1\right)-30=3\left(2a-4\right)$ (Given equation)

$18a+6-30=6a-12$ (Distributive property)

$18a-24=6a-12$ (Simplify)

$18a-24-6a=6a-12-6a$ (Subtract $6a$from both sides)

$12a-24=-12$ (Simplify)

$12a-24+24=-12+24$ (Add 24 to both sides)

$12a=12$ (Simplify)

$\frac{12a}{12}=\frac{12}{12}$ (Divide both sides by 12)

$a=1$ (Simplify)

So, $a=1$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $a=1$in the given equation $6\left(3a+1\right)-30=3\left(2a-4\right)$to get,

$\begin{array}{l}6\left(3+1\right)-30=3\left(2-4\right)\\ 6\left(4\right)-30=3\left(-2\right)\\ 24-30=-6\\ -6=-6\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.