Solution of simple linear equations

We first look at the following question but simpler equations are on the next page.

Question 1

Look at this rule.
P = 4T + 2.
What is the value of T when P = 6?

Solution

P	= 4T + 2
When P	= 6
6	= 4 × T + 2.

We now solve the equation.

6 – 2		= 4 × T + 2 − 2		(Subtract 2 from both sides)
4		= 4 × T
\(\dfrac{4}{4}\)		= \(\dfrac{4\times T}{4}\)		(Divide both sides by 4)
1		= T.

Check: LHS		= 6 and RHS = 4 × 1 + 2 = 6.
LHS		= RHS.

When you are confident some of the steps can be left out.

4 × T + 2		= 6
4 × T		= 4		(Subtract 2 from both sides)
T		= 1.		(Divide both sides by 4)

It is sometimes easy to solve a linear equation just by looking at it.
In fact, this equation can be solved in this manner. It can be seen that T = 1 by inspection.

Solution of simple linear equations

Equations with one operation