Skill: Solve equations involving fractions

Fractions in an equation can make the steps look complicated. A helpful strategy is to clear the denominators by multiplying every term by the least common denominator.

Solve:

$$\frac{3}{4}x-2=\frac{1}{2}x+4$$

1. Find the least common denominator

The denominators are $4$ and $2$, so the least common denominator is $4$.

Multiply every term on both sides by $4$:

$$4\left(\frac{3}{4}x\right)-4(2)=4\left(\frac{1}{2}x\right)+4(4)$$

2. Simplify

The denominators cancel:

$$3x-8=2x+16$$

3. Isolate the variable

Subtract $2x$ from both sides:

$$x-8=16$$

Add $8$ to both sides:

$$x=24$$

4. Check the solution

Substitute $24$ into the original equation:

$$\frac{3}{4}(24)-2=\frac{1}{2}(24)+4$$ $$18-2=12+4$$ $$16=16$$

Both sides are equal, so the solution is

$$\boxed{x=24}$$

Remember: when clearing fractions, multiply every term by the common denominator so the equation remains equivalent.