Question

what is the solution to the equation \\(\frac{3}{4}x = \frac{1}{2}(9x + 150)\\)?
\\(x = \\)

Explanation:

Step1: Eliminate fractions by multiplying both sides by 4 (the least common multiple of 4 and 2).

$$4\times\frac{3}{4}x = 4\times\frac{1}{2}(9x + 150)$$
Simplifying both sides, we get:
$$3x = 2(9x + 150)$$

Step2: Distribute the 2 on the right side.

$$3x = 18x + 300$$

Step3: Subtract \(18x\) from both sides to get all \(x\)-terms on the left.

$$3x - 18x = 18x + 300 - 18x$$
Simplifying, we have:
$$-15x = 300$$

Step4: Divide both sides by \(-15\) to solve for \(x\).

$$x = \frac{300}{-15}$$
Simplifying the fraction, we get:
$$x = -20$$

Answer:

\(-20\)