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

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.