Solving Linear Equations

Solve each equation. Start by selecting an equation and then click "Given".

Step	Operation	Perform	Result
Given			$x + 7 = 13$
	Subtract $7$ from both sides	$x + 7 - 7 = 13 - 7$	$x = 6$

Solution: $x = 6$

Step	Operation	Perform	Result
Given			$18 = 4 x$
	Divide both sides by $4$	$\frac{18}{4} = \frac{4 x}{4}$	$\frac{9}{2} = x$

Solution: $x = \frac{9}{2} = 4 \frac{1}{2}$

Step	Operation	Perform	Result
Given			$2 x - 7 = 15$
	Add $7$ to both sides	$2 x - 7 + 7 = 15 + 7$	$2 x = 22$
	Divide both sides by $2$	$\frac{2 x}{2} = \frac{22}{2}$	$x = 11$

Solution: $x = 11$

Step	Operation	Perform	Result
Given			$2 + 5 x - 5 = 2 x - 14$
	Collect like terms	$2 + 5 x - 5 = 2 x - 14$	$- 3 + 5 x = 2 x - 14$
	Subtract $2 x$ from both sides	$- 3 + 5 x - 2 x = 2 x - 14 - 2 x$	$- 3 + 3 x = - 14$
	Add $3$ to both sides	$- 3 + 3 x + 3 = - 14 + 3$	$3 x = - 11$
	Divide both sides by $3$	$\frac{3 x}{3} = \frac{- 11}{3}$	$x = \frac{- 11}{3}$

Solution: $x = - \frac{11}{3} = - 3 \frac{2}{3}$

Step	Operation	Perform	Result
Given			$3 x + 12 - 4 x + 8 = 5 x + 45 - 2 x + 11$
	Collect like terms on both sides	$3 x + 12 - 4 x + 8 = 5 x + 45 - 2 x + 11$	$- x + 20 = 3 x + 56$
	Add $x$ to both sides	$- x + 20 + x = 3 x + 56 + x$	$20 = 4 x + 56$
	Subtract $56$ from both sides	$20 - 56 = 4 x + 56 - 56$	$- 36 = 4 x$
	Divide both sides by $4$	$\frac{- 36}{4} = \frac{4 x}{4}$	$- 9 = x$

Solution: $x = - 9$

Step	Operation	Perform	Result
Given			$0.05 x + 0.75 = 4 (. 07 x + . 18) + . 72$
	Distribute the " $4$ " across the parenthesis	$0.05 x + 0.75 = 4 (. 07 x + . 18) + . 72$	$0.05 x + 0.75 = . 28 x + . 72 + . 72$
	Subtract $0.05 x$ from both sides	$0.05 x + 0.75 - 0.05 x = . 28 x + . 72 + . 72 - 0.05 x$	$0.75 = . 23 x + . 72 + . 72$
	Collect like terms	$0.75 = . 23 x + . 72 + . 72$	$0.75 = . 23 x + 1.44$
	Subtract $1.44$ from both sides	$0.75 - 1.44 = . 23 x + 1.44 - 1.44$	$- 0.69 = . 23 x$
	Divide both sides by $0.23$	$\frac{- 0.69}{0.23} = \frac{0.23 x}{0.23}$	$- 3 = x$

Solution: $x = - 3$