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

Subtract the constant $4$ from both sides, then divide by the coefficient $3$.

$3x + 4 - 4 = 19 - 4 \;\Rightarrow\; 3x = 15$

Dividing by $3$ gives $x = 5$. Check: $3(5) + 4 = 15 + 4 = 19$, which is true.

Combine the like terms $4x + 3x = 7x$ first, then solve.

$7x + 2 = 30 \;\Rightarrow\; 7x = 28 \;\Rightarrow\; x = 4$

Check in the original: $4(4) + 3(4) + 2 = 16 + 12 + 2 = 30$, which is true.

The constant $6$ is added to $4x$, so subtract it from both sides, then divide by $4$.

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

Dividing by $4$ gives $x = -1$. Check: $6 + 4(-1) = 6 - 4 = 2$, which is true.

Subtract the constant $7$ from both sides, then multiply by the divisor $4$.

$\frac{x}{4} + 7 - 7 = 10 - 7 \;\Rightarrow\; \frac{x}{4} = 3$

Multiplying by $4$ gives $x = 12$. Check: $\frac{12}{4} + 7 = 3 + 7 = 10$, which is true.

The constant $-4$ is the outer layer, so undo it first by adding $4$ to both sides.

$\frac{x}{6} - 4 + 4 = 1 + 4 \;\Rightarrow\; \frac{x}{6} = 5$

Only after the constant is cleared do you multiply by $6$ to undo the division, giving $x = 30$.

Distribute the $5$ across both terms inside the parentheses, then solve.

$5(x + 2) = 5x + 10 = 35 \;\Rightarrow\; 5x = 25 \;\Rightarrow\; x = 5$

Check in the original: $5(5 + 2) = 5(7) = 35$, which is true.

Subtract the constant $1$ from both sides, then divide by the full coefficient $-3$.

$-3x + 1 - 1 = 10 - 1 \;\Rightarrow\; -3x = 9$

A positive divided by a negative is negative, so $x = \frac{9}{-3} = -3$. Check: $-3(-3) + 1 = 9 + 1 = 10$, which is true.

Add the constant $6$ to both sides, then multiply by the divisor $2$.

$\frac{x}{2} - 6 + 6 = -2 + 6 \;\Rightarrow\; \frac{x}{2} = 4$

Multiplying by $2$ gives $x = 8$. Check: $\frac{8}{2} - 6 = 4 - 6 = -2$, which is true.

Test $x = 6$ in each equation, doing the multiplication before the addition.

$3(6) + 4 = 18 + 4 = 22 \;\checkmark$

The others give $2(6) - 1 = 11$, $6 + 6 = 12$, and $5(6) - 2 = 28$, none matching their right side, so only $3x + 4 = 22$ works.

Distribute the $4$ first, then solve the two-step equation.

$4(2x + 1) = 8x + 4 = 20 \;\Rightarrow\; 8x = 16 \;\Rightarrow\; x = 2$

Check in the original: $4(2 \cdot 2 + 1) = 4(5) = 20$, which is true.

Subtract the constant $5$ from both sides, then multiply by the divisor $3$.

$\frac{x}{3} + 5 - 5 = 2 - 5 \;\Rightarrow\; \frac{x}{3} = -3$

Multiplying by $3$ gives $x = -9$. Check: $\frac{-9}{3} + 5 = -3 + 5 = 2$, which is true.

Subtract the constant $8$ from both sides, then divide by $5$.

$5x + 8 - 8 = 2 - 8 \;\Rightarrow\; 5x = -6$

Dividing by $5$ gives $x = -\frac{6}{5}$. Check: $5\left(-\frac{6}{5}\right) + 8 = -6 + 8 = 2$, which is true.