Question

How do you solve `1/3(9x-2) = 1/2(8x-6)`?

Answer 1

`x=7/3`

Explanation:

`color(blue)(1/3(9x-2)=1/2(8x-6)`

Use distributive property

`color(brown)(a(b+c)=ab+ac`

`rarr(1/3 *9x)-(1/3 *2)=(1/2*8x)-(1/2*6)`

Remove the brackets and solve

`rarr1/cancel3^1 *cancel9^3x-1/3 *2=1/cancel2^1*cancel8^4x-1/cancel2^1*cancel6^3`

`rarr3x-2/3=4x-3`

Subtract `3x` both sides

`rarrcancel(3x)-2/3-cancel(3x)=cancel(4x)-3-cancel(3x)`

`rarr-2/3=x-3`

Add `3` both sides

`rarr-2/3+3=xcancel(-3+3`

`color(green)(rArrx=7/3`

Answer 2

`x=7/3`

Explanation:

`1`. Start by factoring out `2` from `(8x-6)`.

`1/3(9x-2)=1/2(8x-6)`

`1/3(9x-2)=1/2*2(4x-3)`

`2`. Simplify the right side of the equation.

`1/3(9x-2)=(4x-3)`

`3`. Multiply both sides of the equation by `3` to get rid of the denominator.

`color(red)3[1/3(9x-2)]=color(red)3(4x-3)`

`4`. Simplify the left side of the equation.

`9x-2=3(4x-3)`

`5`. Expand the bracket.

`9x-2=12x-9`

`6`. Solve for `x`.

`3x=7`

`color(green)(|bar(ul(color(white)(a/a)x=7/3color(white)(a/a)|)))`