Question

assignment: semester 1 review (due unit 7 - solve for x. \\(\frac{3x}{5} + \frac{3}{2} = \frac{4x}{5} + \frac{9}{2}\\) x = \boxed{})

Explanation:

Step1: Eliminate denominators

Multiply all terms by 10 (LCM of 5 and 2):
$$10\times\frac{3x}{5} + 10\times\frac{3}{2} = 10\times\frac{4x}{5} + 10\times\frac{9}{2}$$
Simplify to get:
$$6x + 15 = 8x + 45$$

Step2: Isolate x terms

Subtract $6x$ from both sides:
$$15 = 2x + 45$$

Step3: Isolate constant terms

Subtract 45 from both sides:
$$15 - 45 = 2x$$
$$-30 = 2x$$

Step4: Solve for x

Divide by 2:
$$x = \frac{-30}{2} = -15$$

Answer:

$x = -15$