Solving Multi-Step Equations with Fractions Study Notes

Solve for $x$: $\frac{1}{2}x + \frac{1}{3}x = 10$

$$x = 12$$

Solve for $y$: $\frac{3}{4}y - 2 = \frac{1}{2}y + 3$

$$y = 20$$

Solve for $a$: $\frac{2}{5}a + \frac{1}{10} = \frac{1}{2}a - \frac{3}{10}$

$$a = 4$$

Solve for $m$: $\frac{m}{3} + \frac{m}{4} = 7$

$$m = 12$$

Solve for $k$: $\frac{5}{6}k - \frac{1}{3} = \frac{1}{2}k + \frac{2}{3}$

$$k = 3$$

Solve for $p$: $\frac{2}{3}p + 4 = \frac{5}{9}p + 7$

$$p = 27$$

Solve for $n$: $-2n + \frac{1}{2} = \frac{3}{4}n - 6$

$$n = \frac{26}{11}$$

Solve for $b$: $\frac{1}{5}b + \frac{2}{5}b + 3 = 12$

$$b = 15$$

Solve for $z$: $\frac{3}{8}z - 1 = \frac{1}{4}z + 2$

$$z = 24$$

Solve for $w$: $\frac{7}{12}w - \frac{1}{4} = \frac{1}{3}w + \frac{1}{2}$

$$w = 3$$

Solve for $x$: $\frac{2}{7}x - \frac{5}{14}x = \frac{1}{2}$

$$x = -7$$

Solve for $c$: $\frac{c+2}{4} = \frac{c-1}{3}$

$$c = 10$$

Solve for $d$: $\frac{2d-1}{5} = \frac{d+3}{2}$

$$d = -17$$

Solve for $v$: $\frac{1}{2}v + \frac{2}{3}v - \frac{1}{6}v = 8$

$$v = 8$$

Solve for $t$: $\frac{4}{5}t - 3 = \frac{1}{2}t + 6$

$$t = 30$$

Solve for $h$: $\frac{h}{6} + \frac{h}{9} = 5$

$$h = 18$$

Solve for $r$: $\frac{3}{2}r - \frac{1}{4}r = \frac{5}{8}$

$$r = \frac{1}{2}$$

Solve for $q$: $\frac{q-3}{2} + \frac{q+1}{4} = 5$

$$q = \frac{25}{3}$$

Solve for $x$: $\frac{5}{3}x - 4 = \frac{2}{3}x + 2$

$$x = 6$$

Solve for $g$: $\frac{3g}{10} - \frac{g}{5} = \frac{1}{2}$

$$g = 5$$