Solving linear equations with variables on both sides

All You Need in One Place

Everything you need for Year 6 maths and science through to Year 13 and beyond.

Learn with Confidence

We’ve mastered the national curriculum to help you secure merit and excellence marks.

Unlimited Help

The best tips, tricks, walkthroughs, and practice questions available.

0/1
?
Intros
Lessons
  1. How to turn a word problem into an equation?
    • ex. 1: "revenue" problem
    • ex. 2: "area" problem
0/11
?
Examples
Lessons
  1. Find the solution.
    1. 3.4x=6.33.7x - 3.4x = 6.3 - 3.7x
    2. 37+57x=13x\frac{3}{7} + \frac{5}{7}x = \frac{1}{3}x
    3. 0.42x=0.3x2.670.42x = - 0.3x - 2.67
    4. 56(x+3)=12x\frac{5}{6}\left( {x + 3} \right) = \frac{1}{2}x
    5. 238x=14(2x)2\frac{3}{8}x = \frac{1}{4}\left( {2 - x} \right)
  2. Solve.
    1. 3.61+0.25x=0.111.23x3.61 + 0.25x = 0.11 - 1.23x
    2. 20.1311.6x=3.7+15.2x20.13 - 11.6x = 3.7 + 15.2x
    3. 56x+3=216x - \frac{5}{6}x + 3 = 2 - \frac{1}{6}x
    4. 212x72=314x+342\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.
    1. How long did it take Mary to bike to school?
    2. How far is Mary's home to school?
Topic Notes
?
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.