High School Mathematics 1.19 Linear Equations - One Variable

An equation is an equality connecting with some unknowns.

The unknowns are represented by letters and are called variables.

If the equation has only one unknown, it is called an equation with one variable.

The word Linear means of degree one.

Example:
Divide 64 into two parts such that three times the greater part will be equal to five times the smaller one. Solution:
Let x be the greater part. Then 64 - x is the smaller part.
Then 3x = 5(64 - x)
3x = 320 - 5x
3x + 5x = 320
8x = 320
The two parts are 40 and 24.

Example:
Find a number such that one-fourth of it is less than one-third of it by 4.
Solution:
Let the number be x.
One-fourth of it is less than one-third of it by 4: x/4 + 4 = x/3
x/4 + 4 = x/3
x/4 + 4 = x/3
(x+16)/4 = x/3 ---- multiplying both sides by 12 we have
12 ((x+16)/4) = 12 (x/3)
3x + 48 = 4x
3x + 48 - 3x = 4x - 3x
48 = x
The number is 48.

Directions: Solve the following linear equations. Also write at least 10 examples of your own.