Question

Solve the following equations for x, and give evidence that your solutions are correct (2x/9)+(5/9)=(8/9).

Answer 1

Answer:

The solution is $x=\frac{3}{2}$.

Step-by-step explanation:

We have the following equation $\left(\frac{2x}{9}\right)+\left(\frac{5}{9}\right)=\left(\frac{8}{9}\right)$

To find the value of x, you must:

• Subtract $\frac{5}{9}$ from both sides

$\frac{2x}{9}+\frac{5}{9}-\frac{5}{9}=\frac{8}{9}-\frac{5}{9}$

• Simplify

$\frac{2x}{9}=\frac{1}{3}$

• Multiply both sides by 9

$\frac{2x}{9}\cdot \:9=\frac{1}{3}\cdot \:9$

• Simplify

$2x=3$

• Divide both sides by 2

$\frac{2x}{2}=\frac{3}{2}$

$x=\frac{3}{2}$

To check if this value is a solution of the equation, you substitute the value into the equation and see if the numbers match.

$\left(\frac{2x}{9}\right)+\left(\frac{5}{9}\right)=\left(\frac{8}{9}\right)\\\\\left(\frac{2}{9}\right\cdot x)+\left(\frac{5}{9}\right)=\left(\frac{8}{9}\right)\\\\\left(\frac{2}{9}\right\cdot \frac{3}{2} )+\left(\frac{5}{9}\right)=\left(\frac{8}{9}\right)\\\\\frac{1}{3}+\frac{5}{9}=\frac{8}{9} \\\\\frac{3}{9}+\frac{5}{9}=\frac{8}{9}\\\\\frac{8}{9}=\frac{8}{9}$

Both sides are equal, verifying that $x=\frac{3}{2}$ is a valid solution.