Question

How do you solve `\frac{2x+5}{3}-2=3`?

Answer 1

`x=5`

Explanation:

Add `2` both sides of the equation.

`(2x+5)/3-2color(red)(+2)=3color(red)(+2)`

`(2x+5)/3=5`

Multiply both sides by `3`.

`(2x+5)/3color(red)(xx3)=5color(red)(xx3)`

`2x+5=15`

Subtract `5` from both sides.

`2x+5color(red)(-5)=15color(red)(-5)`

`2x=10`

Divide both sides by `2`.

`(2x)/color(red)(2)=10/color(red)(2)`

`x=5`

Answer 2

`x=5`

Explanation:

`"to eliminate the fraction multiply ALL terms by 3 , the"`
`"denominator of the fraction"`

`cancel(3)^1xx(2x+5)/cancel(3)^1-(3xx2)=3xx3`

`rArr2x+5-6=9larrcolor(red)" no fractions"`

`rArr2x-1=9`

`"add 1 to both sides"`

`2xcancel(-1)cancel(+1)=9+1`

`rArr2x=10`

`"divide both sides by 2"`

`(cancel(2)color(white)(x)x)/cancel(2)=10/2`

`rArrx=5`

`color(blue)"As a check"`

Substitute this value into the left side and if equal to the right side then it is the solution.

`(2xx5+5)/3-2=15/3-2=5-2=3=" right side"`

`rArrx=5" is the solution"`