Question

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

Answer 1

Answer:

Step-by-step explanation:

$\frac{1}{2}(x+15) = 2 + \frac{3}{4}(x-4)$

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

$\frac{1}{2}(34+15) = \frac{49}{2}\\\frac{8}{4} + \frac{3}{4}(34-4) = \frac{8}{4} + \frac{90}{4} = \frac{98}{4} = \frac{49}{2}$

it works