| Linear equations are
also called first degree equations, as the highest power of
the variable in these equations is 1.
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 |
