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Year 10 Interactive Maths - Second Edition


Solving Equations

Linear equations are also called first degree equations, as the highest power of the variable (or pronumeral) in these equations is 1.

E.g. x + 5 = 9 is an equation of the first degree, which is often called a linear equation.

Many problems can be solved by using linear equations.

Recall that:

Equations behave like a balance. So we need to apply the same operation to both sides of an equation to maintain the balance. This means we can:

  • add the same number to both sides of an equation
  • subtract the same number from both sides of an equation
  • multiply both sides of an equation by the same number
  • divide both sides of an equation by the same number


Equations Involving One Operation

Example 1

Solve x + 4 = 9 for x.

Solution:

Subtract 4 from both sides to find x = 5.

Note:

We can check the solution as follows:

LHS = x + 4 = 5 + 4 = 9 = RHS

So, our solution, x = 5, is correct.


Example 2

Solve x - 3 = 7 for x.

Solution:

Add 3 to both sides to find x = 10.

Check:

LHS = x - 3 = 10 - 3 = 7 = RHS

So, our solution, x = 10, is correct.


Example 3

Solve 7x = 21 for x.

Solution:

Divide both sides by 7 to find x = 3.

Check:

LHS = 7x = 7 times 3 = 21 = RHS

So, our solution, x = 3, is correct.


Example 4

Solve x / 3 = 5 for x.

Solution:

Multiply both sides by 3 to find x = 15.

Check:

LHS = x / 3 = 15 / 3 = 5 = RHS

So, our solution, x = 15, is correct.


Key Terms

linear equations, first degree equations, operation


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