Question

How do you solve `\frac { x - 2} { 3} + \frac { 2x + 1} { 4} = 1`?

Answer 1

Taking LCM we get,

Explanation:

`4( x-2) / 3` + `3 (2x + 1 ) / 4`
#4x/12 - 8/12+ 6x/12 + 3 / 12 = 1 #

`4x - 8 +6x +3 = 12`

#10x - 5 = 12 #
`10x = 12 + 5`
`10x = 17`

`x= 17/10 = 1.7`

Answer 2

`x=17/10`

Explanation:

`"multiply through by the lowest common multiple of"`
`"3 and 4 , that is 12"`

`cancel(12)^4xx(x-2)/cancel(3)^1+cancel(12)^3xx(2x+1)/cancel(4)^1=12xx1`

`4(x-2)+3(2x+1)=12larrcolor(blue)"distribute"`

`4x-8+6x+3=12`

`10x-5=12`

`"add 5 to both sides"`

`10x=17`

`"divide both sides by 10"`

`x=17/10`

`color(blue)"As a check"`

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

`(17/10-20/10)/3+(34/10+10/10)/4=-1/10+11/10=1`

`rArrx=17/10" is the solution"`