Question

How do you solve and check `4x + 7( x - 8) = 4( x - 7)`?

Answer 1

`x=4`

Explanation:

To solve the equation, distribute the brackets, collect terms in x on the left side and numeric values on the right side.

distributing brackets.

`4x+7x-56=4x-28`

`rArr11x-56=4x-28`

collecting terms.

subtract 4x from both sides.

`11x-4x-56=cancel(4x)cancel(-4x)-28`

`rArr7x-56=-28`

add 56 to both sides.

`7xcancel(-56)cancel(+56)=-28+56`

`rArr7x=28`

To solve for x, divide both sides by 7

`(cancel(7) x)/cancel(7)=28/7`

`rArrx=4" is the solution"`

`color(red)"As a check"`

If x = 4 is a solution then the equation should be TRUE, that is both sides should be equal.
To test this, substitute x = 4 into the equation and evaluate.

`rArr"left side" =(4xx4)+7(4-8)=16-28=-12`

`"right side " =4(4-7)=4xx-3=-12`

Since both sides are equal then the equation is satisfied and hence x = 4 is the solution.