Example — equation with fractions

Let us see the two principles at work on an equation with denominators. The strategy is to reduce to the same denominator and then get rid of it with the second principle.

Example

Let us solve: $-\frac{x}{2} + 4 = \frac{8}{3} + \frac{x}{3}$ We reduce to the same denominator, which is $6$: $\frac{-3x+24}{6} = \frac{16+2x}{6}$ By the second principle we multiply both sides by $6$: $\begin{aligned} -3x+24 &= 16+2x \\ -5x &= -8 \\ x &= \boxed{\dfrac{8}{5}} \end{aligned}$

Links

Topics: First-degree equations
Concepts: Equation · Principle of equivalence
Methods: First-degree equation
Skills: Calculating · Solving equations