G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

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


| Home Page | Order Maths Software | About the Series | Maths Software Tutorials |
| Year 7 Maths Software | Year 8 Maths Software | Year 9 Maths Software | Year 10 Maths Software |
| Homework Software | Tutor Software | Maths Software Platform | Trial Maths Software |
| Feedback | About mathsteacher.com.au | Terms and Conditions | Our Policies | Links | Contact |

Copyright 2000-2020 mathsteacher.com Pty Ltd.  All rights reserved.
Australian Business Number 53 056 217 611

Copyright instructions for educational institutions

Please read the Terms and Conditions of Use of this Website and our Privacy and Other Policies.
If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number.