Year 9 Interactive Maths - Second Edition

Linear Equations

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

Solving Equations

Recall that:

To solve a linear equation, we do the same operation to both sides of the equation.  This means we can:

• Add the same number to both sides of the equation
• Subtract the same number from both sides of the equation
• Multiply both sides of the equation by the same number
• Divide both sides of the equation by the same number

Equations Involving One Operation

In this section, we will consider equations involving addition, subtraction, multiplication and division.

Equations Involving Addition

Remember that we can subtract the same number from both sides of the equation.

Example 1

Solve x + 3 = 7 for x.

Solution:

Problem Solving

To solve problems, we use the following approach.

Read the problem carefully.  Assume that the unknown number is x (or another suitable pronumeral).  Use the data given in the problem to write an equation.  Then solve the equation for x, and state the answer in words.

Example 2

If a number is increased by 8, the result is 25.  Find the number.

Solution:

Let x be the number.

Increasing x by 8 gives x + 8, which we are told is 25.

So, the number is 17.

Key Terms

linear equations, first degree equations, operation