# Solving linear equations with variables on both sides

### Solving linear equations with variables on both sides

When you want to solve a linear equation with variables on both sides, the first step is to isolate the variables to one side. Once you have done that, we can do subtraction, addition, cross multiplication, or any other necessary steps to solve the equation.

#### Lessons

• Introduction
a)
How to turn a word problem into an equation?
• ex. 1: "revenue" problem
• ex. 2: "area" problem

• 1.
Find the solution.
a)
$- 3.4x = 6.3 - 3.7x$

b)
$\frac{3}{7} + \frac{5}{7}x = \frac{1}{3}x$

c)
$0.42x = - 0.3x - 2.67$

d)
$\frac{5}{6}\left( {x + 3} \right) = \frac{1}{2}x$

e)
$2\frac{3}{8}x = \frac{1}{4}\left( {2 - x} \right)$

• 2.
Solve.
a)
$3.61 + 0.25x = 0.11 - 1.23x$

b)
$20.13 - 11.6x = 3.7 + 15.2x$

c)
$- \frac{5}{6}x + 3 = 2 - \frac{1}{6}x$

d)
$2\frac{1}{2}x - \frac{7}{2} = 3\frac{1}{4}x + \frac{3}{4}$

• 3.
Yesterday, Mary biked to school from home at 9 km/h. Today, she walked to school from home at 3.75 km/h. It took her 37 minutes to go to school on both days altogether.
a)
How long did it take Mary to bike to school?

b)
How far is Mary's home to school?