Question

Solve Quantity x plus 6 end quantity over 2x is equal to three-fourths. Show all work.

Answer 1

The expression described is translated into the following formula:

$\frac{x+6}{2x} = \frac{3}{4}$

Note that this implies that $x \neq 0$

Cross-multiply denominators to get rid of the fractions:

$4(x+6) = 3(2x)$

Expand both sides:

$4x+24 = 6x$

Subtract 4x from both sides:

$24 = 6x - 4x = 2x$

Divide both sides by 2:

$12 = x$

Check:

$\frac{12+6}{24} = \frac{18}{24} = \frac{3}{4}$

Which is true because

$18 \cdot 4= 24\cdot 3$

since both sides evaluate to 72