Question

Solve each equation. Check your solution. (Lesson 2-4)

$\frac{3}{4}w+6=9-\frac{1}{4}-0$

Short answer

The solution of the given equation is $w=\frac{11}{3}$.

Step-by-step solution

Step 1. Given equation.

$\frac{3}{4}w+6=9-\frac{1}{4}-0$

Step 2. Description of step.

In order to solve the given equation first simplify it as:

$$\begin{gathered} \frac{3}{4}w+6=9-\frac{1}{4}-0 \\ \frac{3}{4}w+6=9-\frac{1}{4} \\ \frac{3}{4}w+6=\frac{36-1}{4} \\ \frac{3}{4}w+6=\frac{35}{4} \end{gathered}$$

Now further solve it as:

role="math" localid="1642768295061" $$\begin{gathered} \frac{3}{4}w+6=\frac{35}{4} \\ \frac{3}{4}w=\frac{35}{4}-6 \\ \frac{3}{4}w=\frac{35-24}{4} \\ 3w=\frac{11}{4}\times 4 \\ 3w=11 \\ \Rightarrow w=\frac{11}{3} \end{gathered}$$

Thus,

$w=\frac{11}{3}$

Step 3. Check soultion.

In order to check the solution, put the value of $w=\frac{11}{3}$in the given equation and see if it satisfy the equation, i.e. if left hand side is equals to right hand side, as:

role="math" localid="1642768586323" $$\begin{gathered} \frac{3}{4}w+6=9-\frac{1}{4}-0 \\ \frac{\cancel{3}}{4}\left(\frac{11}{\cancel{3}}\right)+6=\frac{36-1}{4} \\ \frac{11}{4}+6=\frac{35}{4} \\ \Rightarrow \frac{11+24}{4}=\frac{35}{4} \\ \Rightarrow \frac{35}{4}=\frac{35}{4} \\ \Rightarrow \text{True} \end{gathered}$$

Hence, the solution$w=\frac{11}{3}$ satisfies the equation.