Solving One-Step Equations: Practice

The variable is multiplied by $\tfrac{2}{3}$. Dividing by a fraction is multiplying by its reciprocal, so multiply both sides by $\tfrac{3}{2}$.

$\frac{3}{2} \cdot \frac{2}{3}x = \frac{3}{2} \cdot 10 \;\Rightarrow\; x = 15$

Check: $\tfrac{2}{3}(15) = \tfrac{30}{3} = 10$, which is true.

Subtract $\tfrac{3}{4}$ from both sides; the fractions share the denominator $4$.

$x = \tfrac{1}{4} - \tfrac{3}{4} = -\tfrac{2}{4} = -\tfrac{1}{2}$

Check: $-\tfrac{1}{2} + \tfrac{3}{4} = \tfrac{1}{4}$, which is true.

"A number multiplied by $-6$" is $-6x$, and it equals $-48$. Divide both sides by $-6$.

$\frac{-6x}{-6} = \frac{-48}{-6} \;\Rightarrow\; x = 8$

A negative divided by a negative is positive, so $x = 8$. Check: $-6(8) = -48$.

Divide both sides by the coefficient $1.2$.

$\frac{1.2x}{1.2} = \frac{3.6}{1.2} \;\Rightarrow\; x = 3$

Check: $1.2(3) = 3.6$, which is true.

Subtract $7$ from both sides of $b + 7 = 40$ to undo the deposit.

$b + 7 - 7 = 40 - 7 \;\Rightarrow\; b = 33$

Check: $33 + 7 = 40$, which is true.

Multiply both sides by the reciprocal of $-\tfrac{1}{2}$, which is $-2$.

$-2 \cdot \left(-\tfrac{1}{2}x\right) = -2 \cdot 7 \;\Rightarrow\; x = -14$

Check: $-\tfrac{1}{2}(-14) = 7$, which is true.

Subtract $\tfrac{5}{6}$ from both sides. Write $2$ as $\tfrac{12}{6}$ to subtract.

$x = \tfrac{12}{6} - \tfrac{5}{6} = \tfrac{7}{6} = 1\tfrac{1}{6}$

Check: $1\tfrac{1}{6} + \tfrac{5}{6} = 2$, which is true.

Divide both sides of $3w = 13.5$ by $3$.

$\frac{3w}{3} = \frac{13.5}{3} \;\Rightarrow\; w = 4.5$

Check: $3(4.5) = 13.5$, which is true.

The variable still has $5$ subtracted from it, so add $5$ to both sides even though the variable is on the right.

$-8 + 5 = x - 5 + 5 \;\Rightarrow\; -3 = x$

Check: $-3 - 5 = -8$, which is true.

Multiply both sides by the reciprocal $\tfrac{5}{4}$.

$\frac{5}{4} \cdot \frac{4}{5}x = \frac{5}{4} \cdot (-8) \;\Rightarrow\; x = -10$

Check: $\tfrac{4}{5}(-10) = \tfrac{-40}{5} = -8$, which is true.

Divide both sides by $-3$, even though the variable term is on the right.

$\frac{24}{-3} = \frac{-3x}{-3} \;\Rightarrow\; -8 = x$

Check: $-3(-8) = 24$, which is true.

Subtract $2.75$ from both sides.

$x + 2.75 - 2.75 = 2.75 - 2.75 \;\Rightarrow\; x = 0$

Check: $0 + 2.75 = 2.75$, which is true.