Solve x/4 - 3/2 + 2x = 7/2 + 3x for x.

Step-by-step solution

1. 1

   Choose the multiplier that clears every denominator at once. The denominators are $4$ and $2$, so their least common multiple $4$ will do. Multiply every term on both sides — including the whole-number terms $2x$ and $3x$:

   $4\cdot\frac{x}{4}-4\cdot\frac32+4\cdot 2x=4\cdot\frac72+4\cdot 3x$

2. 2

   Carry out the multiplications.

   $x-6+8x=14+12x$

   Forgetting to multiply the non-fraction terms is the classic mistake and would leave an unbalanced equation.

3. 3

   Combine like terms on each side.

   $9x-6=14+12x$

4. 4

   Collect the variable on the side that keeps its coefficient positive. Subtracting $9x$ leaves the $x$ on the right:

   $-6=14+3x\quad\Rightarrow\quad -20=3x$

5. 5

   Solve and check exactly.

   $x=-\frac{20}{3}\approx -6.6667$

   Substituting: the left side is $-\frac{5}{3}-\frac32-\frac{40}{3}=-15-\frac32=-\frac{33}{2}$, and the right side is $\frac72-20=-\frac{33}{2}$. They agree, so $x=-\frac{20}{3}$.