Solving One-Step Equations: Practice

Add $6$ to both sides to undo the subtraction.

$x - 6 + 6 = -2 + 6 \;\Rightarrow\; x = 4$

Check: $4 - 6 = -2$, which is true.

Divide both sides by the full coefficient $-3$, sign included.

$\frac{-3x}{-3} = \frac{21}{-3} \;\Rightarrow\; x = -7$

Check: $-3(-7) = 21$, which is true. A positive divided by a negative is negative.

Multiply both sides by $2$ to undo the division.

$2 \cdot \frac{x}{2} = 2 \cdot (-7) \;\Rightarrow\; x = -14$

Check: $\frac{-14}{2} = -7$, which is true.

Add $\tfrac{1}{3}$ to both sides; the fractions share the denominator $3$.

$x = \tfrac{1}{3} + \tfrac{1}{3} = \tfrac{2}{3}$

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

Subtract $14$ from both sides.

$x + 14 - 14 = 9 - 14 \;\Rightarrow\; x = -5$

Check: $-5 + 14 = 9$, which is true.

The variable is multiplied by $0.4$, so divide both sides by $0.4$.

$\frac{0.4x}{0.4} = \frac{2}{0.4} \;\Rightarrow\; x = 5$

Check: $0.4(5) = 2$, which is true.

Multiply both sides by $5$ to undo the division.

$5 \cdot \frac{x}{5} = 5 \cdot 0.6 \;\Rightarrow\; x = 3$

Check: $\frac{3}{5} = 0.6$, which is true.

Add $12$ to both sides.

$x - 12 + 12 = -12 + 12 \;\Rightarrow\; x = 0$

Check: $0 - 12 = -12$, which is true.

Here $-x$ means $-1$ times $x$, so divide both sides by $-1$ (or multiply by $-1$).

$\frac{-x}{-1} = \frac{6}{-1} \;\Rightarrow\; x = -6$

Check: $-(-6) = 6$, which is true.

Subtract $4$ from both sides.

$x + 4 - 4 = 1 - 4 \;\Rightarrow\; x = -3$

Check: $-3 + 4 = 1$, which is true.

Substitute $7$ for $x$ in the original left side $-2x$.

$-2(7) = -14$

The left side is $-14$, not $14$, so $x = 7$ fails the check. The correct solution is $x = -7$, since $-2(-7) = 14$.

Divide both sides by $9$.

$\frac{9x}{9} = \frac{-27}{9} \;\Rightarrow\; x = -3$

Check: $9(-3) = -27$, which is true.