Respuesta :
Answer:
The solution is [tex]x=\frac{3}{2}[/tex].
Step-by-step explanation:
We have the following equation [tex]\left(\frac{2x}{9}\right)+\left(\frac{5}{9}\right)=\left(\frac{8}{9}\right)[/tex]
To find the value of x, you must:
- Subtract [tex]\frac{5}{9}[/tex] from both sides
[tex]\frac{2x}{9}+\frac{5}{9}-\frac{5}{9}=\frac{8}{9}-\frac{5}{9}[/tex]
- Simplify
[tex]\frac{2x}{9}=\frac{1}{3}[/tex]
- Multiply both sides by 9
[tex]\frac{2x}{9}\cdot \:9=\frac{1}{3}\cdot \:9[/tex]
- Simplify
[tex]2x=3[/tex]
- Divide both sides by 2
[tex]\frac{2x}{2}=\frac{3}{2}[/tex]
[tex]x=\frac{3}{2}[/tex]
To check if this value is a solution of the equation, you substitute the value into the equation and see if the numbers match.
[tex]\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}[/tex]
Both sides are equal, verifying that [tex]x=\frac{3}{2}[/tex] is a valid solution.
