Linear Equations in Disguise: Practice

Multiply every term by the LCD of $2$ and $3$, which is $6$.

$6 \cdot \frac{x}{2} + 6 \cdot \frac{x}{3} = 6 \cdot 5, \qquad 3x + 2x = 30$

Combine like terms and divide: $5x = 30$, so $x = 6$.

Multiply both sides by $6$ to undo the division.

$6 \cdot \frac{x}{6} = 6 \cdot 3, \qquad x = 18$

Multiplying both sides by $10$ clears the decimal.

$10 \cdot 0.1x = 10 \cdot 5, \qquad x = 50$

Multiply both sides by $10$ to clear the decimal, then divide.

$2x = 60, \qquad x = 30$

Multiply every term by $10$ to clear the decimals.

$x + 2 = 5, \qquad x = 3$

Cross-multiply, sending each numerator across to the opposite denominator.

$3x = 6 \cdot 2 = 12, \qquad x = 4$

Cross-multiply.

$2x = 4 \cdot 3 = 12, \qquad x = 6$

Cross-multiply, with $x \neq 0$.

$2 \cdot 4 = 1 \cdot x, \qquad x = 8$

Multiply both sides by $x$ (with $x \neq 0$), then divide by $2$.

$10 = 2x, \qquad x = 5$

Cross-multiply.

$2x = 8, \qquad x = 4$

Multiply both sides by $10$, then divide by $3$.

$3x = 9, \qquad x = 3$

Multiply both sides by $7$ to undo the division.

$x = 7 \cdot 2 = 14$