Question

Solve the equation. Check your solution.

6(w – 4) + 18 = 30

Short answer

The solution is w = 6.

Step-by-step solution

Step 1.Given

The given equation is: $6\left(w-4\right)+18=30$

Step 2.To determine

We have to solve the equation$6\left(w-4\right)+18=30$ and check the solution.

Step 3. Calculation

The given equation is:

$\begin{array}{l}6\left(w-4\right)+18=30\text{(Writeoriginalequation)}\\ 6w-24+18=30\text{(Usedistributiveproperty)}\\ 6w-6=30\text{(Simplify)}\\ 6w-6+6=30+6\text{(Add6toeachsides)}\\ 6w=36\text{(Simplify)}\\ \frac{6w}{6}=\frac{36}{6}\text{(Dividebothsidesby6)}\\ w=6\text{(Simplify)}\end{array}$

To check we will substitute \[w=6\] in left-hand-side of the equation. If the left-hand-side is equal to the right-hand-side then the solution will be correct.

$\begin{array}{l}6\left(w-4\right)+18\\ 6\left(6-4\right)+18\text{(Substitute}w=6\text{)}\\ 30\text{(Simplify)}\end{array}$

We see that, both sides are equal.

This means, the solution is $w=6$.