Solving Two-Step Equations: Practice

The constant $5$ is written first but is still added to $2x$, so subtract it from both sides, then divide by $2$.

$5 + 2x - 5 = 17 - 5 \;\Rightarrow\; 2x = 12$

Dividing by $2$ gives $x = 6$. Check: $5 + 2(6) = 5 + 12 = 17$, which is true.

The variable term is on the right; the constant $3$ is the outer layer, so subtract $3$ from both sides, then divide by $4$.

$19 - 3 = 4x + 3 - 3 \;\Rightarrow\; 16 = 4x$

Dividing by $4$ gives $x = 4$. Check: $4(4) + 3 = 16 + 3 = 19$, which is true.

Subtract $7$ from both sides, then divide by $3$.

$3x + 7 - 7 = 1 - 7 \;\Rightarrow\; 3x = -6$

Dividing by $3$ gives $x = -2$. Check: $3(-2) + 7 = -6 + 7 = 1$, which is true.

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

$4x + 3 - 3 = 9 - 3 \;\Rightarrow\; 4x = 6$

Dividing by $4$ gives $x = \frac{6}{4} = \frac{3}{2}$. Check: $4 \cdot \frac{3}{2} + 3 = 6 + 3 = 9$, which is true.

Subtract the decimal constant $1.5$ from both sides, then divide by $2$.

$2x + 1.5 - 1.5 = 4.5 - 1.5 \;\Rightarrow\; 2x = 3$

Dividing by $2$ gives $x = 1.5$. Check: $2(1.5) + 1.5 = 3 + 1.5 = 4.5$, which is true.

Combine the like terms $3x + 2x = 5x$ first, then solve the two-step equation.

$5x + 4 = 19 \;\Rightarrow\; 5x = 15 \;\Rightarrow\; x = 3$

Check in the original: $3(3) + 2(3) + 4 = 9 + 6 + 4 = 19$, which is true.

Distribute the $2$ across both terms inside the parentheses, then solve.

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

Check in the original: $2(4 + 4) = 2(8) = 16$, which is true.

Subtract the constant $7$ from both sides, then divide by $5$.

$7 + 5x - 7 = 7 - 7 \;\Rightarrow\; 5x = 0$

Dividing by $5$ gives $x = 0$. Check: $7 + 5(0) = 7 + 0 = 7$, which is true.

Add $1$ to both sides, then divide by $6$.

$6x - 1 + 1 = 2 + 1 \;\Rightarrow\; 6x = 3$

Dividing by $6$ gives $x = \frac{3}{6} = \frac{1}{2}$. Check: $6 \cdot \frac{1}{2} - 1 = 3 - 1 = 2$, which is true.

The variable term is on the right; subtract the constant $4$ from both sides, then divide by $3$.

$10 - 4 = 4 + 3x - 4 \;\Rightarrow\; 6 = 3x$

Dividing by $3$ gives $x = 2$. Check: $4 + 3(2) = 4 + 6 = 10$, which is true.

Subtract the constant $4$ from both sides, then multiply by the divisor $3$.

$\frac{x}{3} + 4 - 4 = 2 - 4 \;\Rightarrow\; \frac{x}{3} = -2$

Multiplying by $3$ gives $x = -6$. Check: $\frac{-6}{3} + 4 = -2 + 4 = 2$, which is true.

Subtract the constant $6$ from both sides. The coefficient of $x$ is $-1$, so divide by $-1$.

$-x + 6 - 6 = 10 - 6 \;\Rightarrow\; -x = 4$

Dividing by $-1$ gives $x = -4$. Check: $-(-4) + 6 = 4 + 6 = 10$, which is true.