# Linear Equation (One Variable)

See how to solve a linear equation/inequality (one variable).

7 examples and their solutions.

## Linear Equation (One Variable)

### Example

x + 2 = 3

x + 2 = 3 means□ + 2 = 3.

So solving an equation is

finding the number that can be filled in □.

Solution

x + 2 = 3

x = 3 - 2 - [1] [2]

= 1

x = 3 - 2 - [1] [2]

= 1

[1]

Move +2 to the right side.

Then write, the opposite of +2,

-2 on the right side.

Then write, the opposite of +2,

-2 on the right side.

[2]

x + 2 = 3

x + 2 - 2 = 3 - 2

x = 3 - 2

x + 2 - 2 = 3 - 2

x = 3 - 2

Close

### Example

x - 1 = 8

Solution x - 1 = 8

x = 8 + 1 - [1] [2]

= 9

x = 8 + 1 - [1] [2]

= 9

[1]

Move -1 to the right side.

Then write, the opposite of -1,

+1 on the right side.

Then write, the opposite of -1,

+1 on the right side.

[2]

x - 1 = 8

x - 1 + 1 = 8 + 1

x = 8 + 1

x - 1 + 1 = 8 + 1

x = 8 + 1

Close

### Example

7x = 35

Solution 7x = 35

x = 357- [1]

= 5

x = 357- [1]

= 5

[1]

÷7 both sides.

Close

### Example

-x4 = 9

Solution -x4 = 9

x = 9⋅(-4) - [1]

= -36

x = 9⋅(-4) - [1]

= -36

[1]

×(-4) both sides.

Close

### Example

5x + 8 = 2x - 13

Solution 5x + 8 = 2x - 13

5x - 2x = -13 - 8 - [1]

3x = -21

x = -213 - [2]

= -7

5x - 2x = -13 - 8 - [1]

3x = -21

x = -213 - [2]

= -7

[1]

Move +8 to the right side.

And move 2x to the left side.

And move 2x to the left side.

[2]

÷3 both sides.

Close

## Linear Inequality (One Variable)

### Example

7x + 5 ≥ 19

Solution 7x + 5 ≥ 19

7x ≥ 19 - 5

7x ≥ 14

x ≥ 147 - [1]

x ≥ 2

7x ≥ 19 - 5

7x ≥ 14

x ≥ 147 - [1]

x ≥ 2

[1]

÷7 both sides.

7 is (+).

So the order of the inequality sign

doesn't change.

≥ → ≥

When multiplying or dividing (+) on both sides,

the inequality sign doesn't change.

7 is (+).

So the order of the inequality sign

doesn't change.

≥ → ≥

When multiplying or dividing (+) on both sides,

the inequality sign doesn't change.

Close

### Example

2 - 3x < 8

Solution 2 - 3x < 8

-3x < 8 - 2

-3x < 6

x > 6-3

x > -2

-3x < 8 - 2

-3x < 6

x > 6-3

x > -2

[1]

÷(-3) to both sides.

-3 is (-).

So the order of the inequality sign

does change.

< → >

When multiplying or dividing (-) on both sides,

the inequality sign does change.

-3 is (-).

So the order of the inequality sign

does change.

< → >

When multiplying or dividing (-) on both sides,

the inequality sign does change.

Close