Question

How do you solve `3( x + 8) = 2( 4x + 22)`?

Answer 1

`x=-4`

Refer to the explanation for the process.

Explanation:

Solve:

`3(x+8)=2(4x+22)`

Expand the left-hand side using the distributive property: `a(b+c)=ab+ac`.

`3x+24=2(4x+22)`

Expand the right-hand side.

`3x+24=8x+44`

Subtract `24` from both sides.

`3x=8x+44-24`

Simplify.

`3x=8x+20`

Subtract `8x` from both sides.

`3x-8x=20`

Simplify.

`-5x=20`

Divide both sides by `-5`.

`x=20/(-5)`

Simplify.

`x=-20/5`

Reduce `-20/5` by dividing the numerator by the denominator.

`x=-color(red)cancel(color(black)(20))^4/color(red)cancel(color(black)(5))^1`

`x=-4`