Question

1. $\frac{2}{3}x - 5 = 2+\frac{3}{2}x$

Explanation:

Step1: Move terms with x to one - side

Subtract $\frac{1}{2}x$ from both sides and add 5 to both sides: $\frac{2}{3}x-\frac{1}{2}x=2 + 5$.

Step2: Find a common denominator for x - terms

The common denominator of 3 and 2 is 6. So, $\frac{2\times2}{3\times2}x-\frac{1\times3}{2\times3}x=7$, which simplifies to $\frac{4}{6}x-\frac{3}{6}x=7$.

Step3: Combine x - terms

$\frac{4x - 3x}{6}=7$, or $\frac{x}{6}=7$.

Step4: Solve for x

Multiply both sides by 6: $x = 42$.

Answer:

$x = 42$