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

2 Answers
Apr 10, 2016

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

Apr 10, 2016

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)|)))