KS3 Maths

Previous Topic
Next Topic

Solving Equations With Variables on One Side

KS3 Maths Algebra Solving Equations With Variables on One Side

An equation consists of two sides separated by an equals sign. When all the variables are on one side, your main task is to isolate the variable on that side of the equation. This allows you to find its value.

The goal is to perform the same operation on both sides of the equation to maintain balance, just like you would with a real-life scale.

One-Step Equations

These are equations that can be solved in a single step. For instance:

Example: x + 3 = 7

  • Step 1: Subtract 3 from both sides of the equation to isolate x
  • Result: x = 4

Two-Step Equations

For two-step equations, you’ll need two operations to isolate the variable.

Example: 2x + 3 = 9

  • Step 1: Subtract 3 from both sides to get rid of the constant term on the side with x, which forms 2x = 6
  • Step 2: Divide both sides by 2 to isolate x: x = 3

Equations with More Than Two Steps

Sometimes equations are more complex and require more than two steps to solve. Let’s look at two examples.

Example: 3x + 5 - 1 = 10

  • Step 1: Combine like terms on the variable side: 3x + 4 = 10.
  • Step 2: Eliminate the constant on the variable side by subtracting 3 from both sides: 3x = 6
  • Step 3: Divide both sides by 3 to solve for x: x = \frac{6}{3}

Therefore, the result is x = 2

These types of equations might look intimidating at first, but they can be solved by applying the same principles: isolating the variable by maintaining the balance of both sides of the equation. With practice, solving equations with more than two steps becomes more straightforward.

Practice Questions

Question 1:

Solve x + 5 = 10

Subtract 5 from both sides to get x = 5

Question 2:

Solve 3x = 15

Divide both sides by 3 to get x = 5

Question 3:

Solve 4x + 2 = 18

First, subtract 2 from both sides to get 4x = 16

Then, divide both sides by 4 to find x = 4

Question 4:

Solve 6x + 9 - 3 = 12

Step 1: Combine like terms on the side of the equation with the variable. 6x + 9 - 3 simplifies to 6x + 6. The right side, 12, is already simplified.

Step 2: Eliminate the constant term from the side containing the variable. Subtract 6 from both sides of the equation to get 6x = 6.

Step 3: Divide both sides by 6 to solve for x: x = \frac{6}{6}, which simplifies to x = 1.

Previous Topic
Back to Lesson
Next Topic