Linear Equation (One Variable)
How to solve a linear equation (one variable): 5 examples and their solutions.
Examplex + 2 = 3
x + 2 = 3 means
[blank] + 2 = 3.
So solving an equation is
finding the value of the [blank].
So the goal is
to find the value of x.
To find the value of x,
the equation should look like
[x = ...].
But the left side is x + 2, not x.
So, to remove +2 in the left side,
move +2 to the right side.
When a term moves to the other side,
its sign changes.
Then the left side is x.
And the right side is
3,
change the sign of +2, -2.
3 - 2 = 1
So x = 1.
Examplex - 1 = 8
The left side is x - 1.
To remove -1 in the left side,
move -1 to the right side.
When a term moves to the other side,
its sign changes.
Then the left side is x.
And the right side is
8,
change the sign of -1, +1.
8 + 1 = 9
So x = 9.
Example7x = 35
The left side is 7x.
To remove 7 in the left side,
divide both sides by 7.
Then the left side is x.
And the right side is 35/7.
35/7 = 5
So x = 5.
Example-x/4 = 9
The left side is -x/4.
So, to remove (-) and /4,
multiply (-4) to both sides.
Then the left side is x.
And the right side is 9⋅(-4).
9⋅(-4) = -36
So x = -36.
Example5x + 8 = 2x - 13
Move the x terms in the left side.
And move the other terms in the right side.
So move +8 to the right side.
And move 2x to the left side.
Then the left side is
5x,
change the sign of 2x, -2x.
And the right side is
-13,
change the sign of +8, -8.
5x - 2x = 3x
-13 - 8 = -21
To remove 3 in the left side,
divide both sides by 3.
Then the left side is x.
And the right side is -21/3.
-21/3 = 7
So x = -7.