Solving One-Step Equations: Additional Practice (Set 1)

Subtract $17$ from both sides.

$x + 17 - 17 = 5 - 17 \;\Rightarrow\; x = -12$

Check: $-12 + 17 = 5$, which is true.

Divide both sides by the full coefficient $-7$.

$\frac{-7x}{-7} = \frac{28}{-7} \;\Rightarrow\; x = -4$

Check: $-7(-4) = 28$, which is true.

Add $0.8$ to both sides.

$x - 0.8 + 0.8 = 2.7 + 0.8 \;\Rightarrow\; x = 3.5$

Check: $3.5 - 0.8 = 2.7$, which is true.

Multiply both sides of $\dfrac{L}{4} = 2.25$ by $4$.

$4 \cdot \frac{L}{4} = 4 \cdot 2.25 \;\Rightarrow\; L = 9$

Check: $\frac{9}{4} = 2.25$, which is true.

Multiply both sides by $7$ to undo the division.

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

Check: $\frac{-21}{7} = -3$, which is true.

The variable is divided by $6$, so the inverse is to multiply both sides by $6$, not divide.

$6 \cdot \frac{x}{6} = 6 \cdot 4 \;\Rightarrow\; x = 24$

Mara divided ($4 \div 6$) and got $\tfrac{2}{3}$. The correct solution is $x = 24$, since $\frac{24}{6} = 4$.

Divide both sides by $2.5$.

$\frac{2.5x}{2.5} = \frac{-10}{2.5} \;\Rightarrow\; x = -4$

Check: $2.5(-4) = -10$, which is true.

Add $12$ to both sides of $p - 12 = 35$ to undo the markdown.

$p - 12 + 12 = 35 + 12 \;\Rightarrow\; p = 47$

Check: $47 - 12 = 35$, which is true.

Subtract $6.5$ from both sides.

$x + 6.5 - 6.5 = 6.5 - 6.5 \;\Rightarrow\; x = 0$

Check: $0 + 6.5 = 6.5$, which is true.

Multiply both sides by $2.5$ to undo the division.

$2.5 \cdot \frac{x}{2.5} = 2.5 \cdot 4 \;\Rightarrow\; x = 10$

Check: $\frac{10}{2.5} = 4$, which is true.

The term $-x$ means $-1$ times $x$, so multiply (or divide) both sides by $-1$ to make the coefficient $+1$.

$-1 \cdot (-x) = -1 \cdot (-13) \;\Rightarrow\; x = 13$

Check: $-(13) = -13$, which is true.

Multiplying by $\tfrac{1}{4}$ is the same as dividing by $4$, so multiply both sides by $4$ (the reciprocal of $\tfrac{1}{4}$).

$4 \cdot \frac{1}{4}x = 4 \cdot 6 \;\Rightarrow\; x = 24$

Check: $\tfrac{1}{4}(24) = 6$, which is true.