Question

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

Answer 1

The solution is
`x=(3)/(2)`.

Explanation:

We have the following equation
`\left((2x)/(9)\right)+\left((5)/(9)\right)=\left((8)/(9)\right)`

To find the value of x, you must:

• Subtract
  `(5)/(9)` from both sides

`(2x)/(9)+(5)/(9)-(5)/(9)=(8)/(9)-(5)/(9)`

• Simplify

`(2x)/(9)=(1)/(3)`

• Multiply both sides by 9

`(2x)/(9)\cdot \:9=(1)/(3)\cdot \:9`

• Simplify

`2x=3`

• Divide both sides by 2

`(2x)/(2)=(3)/(2)`

`x=(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((2x)/(9)\right)+\left((5)/(9)\right)=\left((8)/(9)\right)\\\\\left((2)/(9)\right\cdot x)+\left((5)/(9)\right)=\left((8)/(9)\right)\\\\\left((2)/(9)\right\cdot (3)/(2) )+\left((5)/(9)\right)=\left((8)/(9)\right)\\\\(1)/(3)+(5)/(9)=(8)/(9) \\\\(3)/(9)+(5)/(9)=(8)/(9)\\\\(8)/(9)=(8)/(9)`

Both sides are equal, verifying that
`x=(3)/(2)` is a valid solution.