A linear equation in one variable is an equation that can be written in the form ax=b where a and b are constants and a≠0.

Example 1

Solve 5n + 11 = 7n - 9

Solution:

5n + 11 = 7n - 9 Write original equation.

5n - 5n + 11 = 7n - 5n - 9 Subtract 5n from each side.

11 = 2n - 9

11 + 9 = 2n - 9 + 9 Add 9 to each side.

20 = 2n

20/2 = 2n/2 Divide each side by 2.

10 = n

The solution is 10.

Checking:

n = 10

5n + 11 = 7n - 9

5(10) + 11 = 7(10) - 9

0 + 11 = 70 - 9

✓

61 = 61

Example 2

Solve 8x - 5 = 19

Solution:

8x - 5 = 19 Write the original equation.

8x - 5 + 5 = 19 + 5 Add 5 from each side.

8x = 24

8x/8 = 24/8 Divide each side by 8.

x = 3

The solution is 3.

Checking:

x = 3

8x - 5 = 19

8(3) - 5 = 19

24 - 5 = 19

✓

19 = 19

Example 3

Solve 2t + 2 = 27 - 3t

Solution:

2t + 2 = 27 - 3t Write the original equation.

2t + 3t +2 = 27-3t + 3t Add 3t from each side.

5t + 2 = 27

5t + 2 - 2 = 27 - 2 Subtract 2 to each side.

5t/5 = 25/5 Divide each side by 5.

t = 5

The solution is 5.

Checking:

t = 5

2t + 2= 27 - 3t

2(5) + 2 = 27 - 3(5)

10 + 2 = 27 - 15

✓

12 = 12

There are expressions and equations given. We will point out an expression/equation if the expression/equation;

has only a CONSTANT, you have to LEAN to the RIGHT

has only a VARIABLE, you have to LEAN to the LEFT

is a term with ONE VARIABLE, you have to STAND

is a term with TWO VARIABLE, you have to SIT DOWN