Solving Two-Step Equations: Practice

Combine the like terms $7x + 2x = 9x$ first, then solve the two-step equation.

$9x - 5 = 13 \;\Rightarrow\; 9x = 18 \;\Rightarrow\; x = 2$

Check in the original: $7(2) + 2(2) - 5 = 14 + 4 - 5 = 13$, which is true.

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

$5(x - 2) = 5x - 10 = 35 \;\Rightarrow\; 5x = 45 \;\Rightarrow\; x = 9$

Check in the original: $5(9 - 2) = 5(7) = 35$, which is true.

Add the constant $7$ to both sides, then divide by the full coefficient $-4$.

$-4x - 7 + 7 = 5 + 7 \;\Rightarrow\; -4x = 12$

A positive divided by a negative is negative, so $x = \frac{12}{-4} = -3$. Check: $-4(-3) - 7 = 12 - 7 = 5$, which is true.

Test $x = 5$ in each equation by substituting and evaluating with the order of operations.

$3(5) - 1 = 15 - 1 = 14 \;\checkmark$

The others give $2(5) + 3 = 13$, $4(5) + 2 = 22$, and $5 + 5 = 10$, none of which equal their right side, so only $3x - 1 = 14$ works.

Distribute the $2$ first, then solve the two-step equation.

$2(3x + 1) = 6x + 2 = 20 \;\Rightarrow\; 6x = 18 \;\Rightarrow\; x = 3$

Check in the original: $2(3 \cdot 3 + 1) = 2(10) = 20$, which is true.

Add the constant $2$ to both sides, then multiply by the divisor $5$.

$\frac{x}{5} - 2 + 2 = -4 + 2 \;\Rightarrow\; \frac{x}{5} = -2$

Multiplying by $5$ gives $x = -10$. Check: $\frac{-10}{5} - 2 = -2 - 2 = -4$, which is true.

Subtract the constant $9$ from both sides, then divide by the full coefficient $-2$.

$9 - 2x - 9 = 3 - 9 \;\Rightarrow\; -2x = -6$

A negative divided by a negative is positive, so $x = \frac{-6}{-2} = 3$. Check: $9 - 2(3) = 9 - 6 = 3$, which is true.

Subtract $3$ from both sides, then divide by $10$.

$10x + 3 - 3 = 8 - 3 \;\Rightarrow\; 10x = 5$

Dividing by $10$ gives $x = \frac{5}{10} = \frac{1}{2}$. Check: $10 \cdot \frac{1}{2} + 3 = 5 + 3 = 8$, which is true.

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

$4(2x - 3) = 8x - 12 = 4 \;\Rightarrow\; 8x = 16 \;\Rightarrow\; x = 2$

Check in the original: $4(2 \cdot 2 - 3) = 4(1) = 4$, which is true.

Test $x = -4$ in each equation, evaluating the multiplication before the addition.

$5(-4) + 8 = -20 + 8 = -12 \;\checkmark$

The others give $2(-4) + 5 = -3$, $3(-4) - 2 = -14$, and $-4 - 4 = -8$, none matching their right side, so only $5x + 8 = -12$ works.

Add the constant $2$ to both sides, then divide by the coefficient $1.5$.

$1.5x - 2 + 2 = 4 + 2 \;\Rightarrow\; 1.5x = 6$

Dividing by $1.5$ gives $x = \frac{6}{1.5} = 4$. Check: $1.5(4) - 2 = 6 - 2 = 4$, which is true.

Combine the like terms $2x + 6x = 8x$ first, then solve the two-step equation.

$8x - 4 = 12 \;\Rightarrow\; 8x = 16 \;\Rightarrow\; x = 2$

Check in the original: $2(2) + 6(2) - 4 = 4 + 12 - 4 = 12$, which is true.