When solving equations involving fractions, it's usually easiest to clear fractions first
by multiplying by the least common denominator of all the fractions involved,
as illustrated in the examples below.
$\displaystyle\frac{2}{3}x + 6 = 1$ | (original equation) |
$\displaystyle3\left(\frac{2}{3}x + 6\right) = 3(1)$ | (multiply both sides by $\,3\,$) |
$2x + 18 = 3$ | (simplify; all fractions are gone) |
$2x = -15$ | (subtract $\,18\,$ from both sides) |
$\displaystyle x = -\frac{15}{2}$ | (divide both sides by $\,2\,$) |
$\displaystyle -3x -\frac{8}{9} = \frac{5}{6}$ | (original equation) |
$\displaystyle 18\left(-3x -\frac{8}{9}\right) = 18(\frac{5}{6})$ | (multiply both sides by $\,18\,$, which is the least common multiple of $\,9\,$ and $\,6\,$) |
$-54x - 16 = 15$ | (simplify; all fractions are gone) |
$-54x = 31$ | (add $\,16\,$ to both sides) |
$\displaystyle x = -\frac{31}{54}$ | (divide both sides by $\,-54\,$) |
For more advanced students, a graph is displayed.
For example, the equation $\,\frac{2}{3}x + 6 = 1\,$
is optionally accompanied by the
graph of $\,y = \frac{2}{3}x + 6\,$ (the left side of the equation, dashed green)
and the graph of
$\,y = 1\,$ (the right side of the equation, solid purple).
Notice that you are finding the value of $\,x\,$ where these graphs intersect.
Click the “show/hide graph” button if you prefer not to see the graph.