Question

Which value of x makes the equation 0.5(x + 15) = 2 + 0.75(x - 4) true?

Answer 1

Explanation:

`(1)/(2)(x+15) = 2 + (3)/(4)(x-4)`

To make this easier, to get ride of the fractions, we can multiply both sides by 4

`2(x+15) = 8 + 3(x-4)`

now use the distributive property

`2x + 30 = 8 + 3x - 12\\`

now we want to isolate x to one side and isolate all the constants to the other

`2x - 3x = 8 - 12 - 30\\`

now simplify

`-x = -34\\x = 34`

to test, we can plug in back to the original

`(1)/(2)(34+15) = (49)/(2)\\(8)/(4) + (3)/(4)(34-4) = (8)/(4) + (90)/(4) = (98)/(4) = (49)/(2)`

it works