Q18. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{5}{9}+w=\frac{7}{9}$

Step-by-Step Solution

Answer

The solution of the equation is $w=\frac{2}{9}$.

Step-1. Apply the concept of addition and subtraction of equality.

An equation is an expression containing two quantities separated by a = symbol.

Finding solution to an equation involves separating the variable on one side of the equation and numbers on the other side.

We can add or subtract by same quantities on both sides of the equation for separating the variable on one side of the equation and the numbers on the other side.

For example, in the equation below we add 5 to both sides of the equation to find a solution:

$\begin{array}{l}x-5=3\\ x-5+5=3+5\end{array}$

We are given the equation $\frac{5}{9}+w=\frac{7}{9}$, we subtract $\frac{5}{9}$ to both sides of the equation as shown:

$\frac{5}{9}+w-\frac{5}{9}=\frac{7}{9}-\frac{5}{9}$

Step-2. Simplify the expression.

We subtracted $\frac{5}{9}$ to both sides of the equation and obtained:

$\frac{5}{9}+w-\frac{5}{9}=\frac{7}{9}-\frac{5}{9}$

Next we simplify the expression as shown:

$\begin{array}{l}\frac{5}{9}+w-\frac{5}{9}=\frac{7}{9}-\frac{5}{9}\\ w=\frac{7}{9}-\frac{5}{9}\end{array}$

Step-3. Write the solution.

$\begin{array}{l}w=\frac{7}{9}-\frac{5}{9}\\ w=\frac{7-5}{9}\\ w=\frac{2}{9}\end{array}$

Thus, the solution of the equation is $w=\frac{2}{9}$.

Step-4. Checking the solution.

We substitute the value of the variable into the given equation:

$\begin{array}{l}\frac{5}{9}+w=\frac{7}{9}\\ \frac{5}{9}+\frac{2}{9}=\frac{7}{9}\\ \frac{7}{9}=\frac{7}{9}\end{array}$

Since the above equation is satisfied, the solution $w=\frac{2}{9}$ is verified.