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