Solving Two-Step Equations: Practice

Subtract the constant $3$ from both sides, then divide by the coefficient $2$.

$2x + 3 - 3 = 11 - 3 \;\Rightarrow\; 2x = 8$

Dividing by $2$ gives $x = 4$. Check: $2(4) + 3 = 8 + 3 = 11$, which is true.

Subtract $1$ from both sides, then divide by $3$.

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

Dividing by $3$ gives $x = 3$. Check: $3(3) + 1 = 9 + 1 = 10$, which is true.

Add $2$ to both sides, then divide by $5$.

$5x - 2 + 2 = 13 + 2 \;\Rightarrow\; 5x = 15$

Dividing by $5$ gives $x = 3$. Check: $5(3) - 2 = 15 - 2 = 13$, which is true.

Subtract $4$ from both sides, then divide by $6$.

$6x + 4 - 4 = 22 - 4 \;\Rightarrow\; 6x = 18$

Dividing by $6$ gives $x = 3$. Check: $6(3) + 4 = 18 + 4 = 22$, which is true.

Subtract $2$ from both sides, then divide by $7$.

$7x + 2 - 2 = 23 - 2 \;\Rightarrow\; 7x = 21$

Dividing by $7$ gives $x = 3$. Check: $7(3) + 2 = 21 + 2 = 23$, which is true.

The variable is multiplied by the coefficient $4$, so divide both sides by $4$.

$\frac{4x}{4} = \frac{20}{4} \;\Rightarrow\; x = 5$

Subtracting $4$ would not help, because $4x$ means $4$ times $x$, not $4$ plus $x$.

Add the constant $2$ to both sides, then multiply by the divisor $3$.

$\frac{x}{3} - 2 + 2 = 1 + 2 \;\Rightarrow\; \frac{x}{3} = 3$

Multiplying by $3$ gives $x = 9$. Check: $\frac{9}{3} - 2 = 3 - 2 = 1$, which is true.

Substitute $5$ for $x$ in the original left side, doing the multiplication before the addition.

$3(5) + 2 = 15 + 2 = 17$

The left side equals $17$, the same as the right side, so the solution checks out.

Subtract $8$ from both sides, then divide by $4$.

$4x + 8 - 8 = 20 - 8 \;\Rightarrow\; 4x = 12$

Dividing by $4$ gives $x = 3$. Check: $4(3) + 8 = 12 + 8 = 20$, which is true.

Add $7$ to both sides, then divide by $2$.

$2x - 7 + 7 = 3 + 7 \;\Rightarrow\; 2x = 10$

Dividing by $2$ gives $x = 5$. Check: $2(5) - 7 = 10 - 7 = 3$, which is true.

The constant $3$ is the outer layer, so undo it first by subtracting $3$ from both sides.

$\frac{x}{5} + 3 - 3 = 4 - 3 \;\Rightarrow\; \frac{x}{5} = 1$

Only after the constant is cleared do you multiply by $5$ to undo the division.

Add $5$ to both sides, then divide by $6$.

$6x - 5 + 5 = 7 + 5 \;\Rightarrow\; 6x = 12$

Dividing by $6$ gives $x = 2$. Check: $6(2) - 5 = 12 - 5 = 7$, which is true.