Solving Linear Equations: Practice

Undo the addition of $7$ by subtracting it from both sides.

$x + 7 - 7 = 12 - 7, \qquad x = 5$

Undo the subtraction by adding $3$ to both sides.

$x - 3 + 3 = 8 + 3, \qquad x = 11$

Undo the multiplication by dividing both sides by $4$.

$\frac{4x}{4} = \frac{20}{4}, \qquad x = 5$

Solve by adding $5$ and dividing by $3$.

$3x = 12, \qquad x = 4$

Substituting back, $3(4) - 5 = 7$, so $x = 4$ makes the statement true.

Add $4$ to both sides, then divide by $6$.

$6x = 18, \qquad x = 3$

Subtract $1$ from both sides, then multiply by $2$.

$\frac{x}{2} = 4, \qquad x = 8$

Add $2$ to both sides to isolate $x$.

$7 + 2 = x, \qquad x = 9$

Divide both sides by $2$.

$x = \frac{-8}{2} = -4$

Subtract $10$ from both sides, then multiply by $-1$.

$-x = -6, \qquad x = 6$

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

$6 = 2x, \qquad x = 3$

Divide both sides by $9$.

$x = \frac{0}{9} = 0$

Undo the operations in reverse order. The last operation done to $x$ is adding $5$, so undo it first by subtracting $5$ from both sides.

$2x + 5 - 5 = 17 - 5, \qquad 2x = 12$

Dividing by $2$ comes afterward, giving $x = 6$.