Question

given $3 - \frac{4x}{5} - \frac{8 - 2x}{4} = 0$, what is $x$?
a $-\frac{37}{2}$
b $\frac{10}{3}$
c $8$
d $\frac{50}{3}$

Explanation:

Step1: Eliminate denominators

Multiply all terms by 20 (LCM of 5 and 4):
$$20\times3 - 20\times\frac{4x}{5} - 20\times\frac{8-2x}{4} = 20\times0$$
$$60 - 16x - 5(8-2x) = 0$$

Step2: Expand the parentheses

Distribute the -5 to terms inside:
$$60 - 16x - 40 + 10x = 0$$

Step3: Combine like terms

Combine constant terms and x terms:
$$(60-40) + (-16x+10x) = 0$$
$$20 - 6x = 0$$

Step4: Isolate the x term

Rearrange to move constants to one side:
$$-6x = -20$$

Step5: Solve for x

Divide both sides by -6:
$$x = \frac{-20}{-6} = \frac{10}{3}$$

Answer:

B. $\frac{10}{3}$