Question

How do you solve `5(x+2) = 7(x-2)`?

Answer 1

`x=12`

Explanation:

distribute the brackets on both sides of the equation.

`rArr5x+10=7x-14`

collect terms in x on the left side and numeric values on the right side.

subtract 7x from both sides.

`5x-7x+10=cancel(7x)cancel(-7x)-14`

`rArr-2x+10=-14`

subtract 10 from both sides.

`-2xcancel(+10)cancel(-10)=-14-10`

`rArr-2x=-24`

To solve for x, divide both sides by - 2

`(cancel(-2) x)/cancel(-2)=(-24)/(-2)`

`rArrx=12`

`color(blue)"As a check"`

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

`"left side "=5(12+2)=5xx14=70`

`"right side "=7(12-2)=7xx10=70`

`rArrx=12" is the solution"`