Question

How do you solve the system of equations `\frac { 2x - 5} { 4} + x = \frac { 2x + 5} { 2} + 4`?

Answer 1

`x=15 1/2`

Explanation:

`(2x-5)/4 +x=(2x+5)/2+4`

Multiply both sides by `4` and simplify.

`2x-5+4x=2(2x+5)+16`

Further simplify by opening the brackets and combining terms.

`6x-5=4x+10+16`

`6x-5=4x+26`

Shift terms and simplify.

`6x-4x=26+5`

`2x=31`

Divide both sides by `2`

`x=31/2= 15 1/2`

Answer 2

`x=31/2`

Explanation:

To solve this equation take same common denominator in both sides.
Common denominator is `color(red)(L.C.M(2,4)=4`

`(2x-5)/4+x=(2x+5)/2+4`

`rArr(2x-5)/4+(color(red)4*x)/4=(color(red)2(2x+5))/4+16/4`

`rArr2x-5+4x=2(2x+5)+16`

`rArr6x-5=4x+10+16`

`rArr6x-4x=5+10+16`

`rArr2x=31`

`rArrx=31/2`