Question

How do you solve `8(x+3) = 5x-(14-2x)+48`?

Answer 1

`color(maroon(x = 10`

Explanation:

`8(x + 3) = 5x - (14 - 2x) + 48`

`8x + 24 = 5x - 14 + 2x + 48, " removing braces"`

`8x - 5x - 2x = -14 + 48 - 24, " bringing like terms together"`

`color(maroon(x = 10`

Answer 2

`x = 10`

Explanation:

`8(x+3) = 5x - (14-2x) = 48`

First, use the distributive property (shown below) to simplify `8(x+3)` and `-(14-2x)`

Following this image, we know that:
`color(blue)(8(x+3) = (8 * x) + (8 * 3) = 8x + 24)`
and
`color(blue)(-(14-2x) = -14 + 2x)`

Put them back into the equation:
`8x + 24 = 5x - 14 + 2x + 48`

Combine like terms on the right hand side:
`8x + 24 = 7x + 34`

Subtract `color(blue)(7x)` from both sides:
`8x + 24 quadcolor(blue)(-quad7x) = 7x + 34 quadcolor(blue)(-quad7x)`

`x + 24 = 34`

Subtract `color(blue)24` from both sides:
`x + 24 quadcolor(blue)(-quad24) = 34 quadcolor(blue)(-quad24)`

Therefore,
`x = 10`

Hope this helps!