1. Remove parentheses by multiplying (this step is not always
necessary)
2. Collect like terms on each side of the equal sign
3. Isolate the variable by "undoing" the operation
(do this until the variable is by itself)
"undo" addition and subtraction first
next, "undo" multiplication and division
4. Check by substituting the solution into the original
equation
Example 1
3x + 4 = 10
This equation will require 2 steps to
solve it
3x + 4 -4 = 10 -4
First, we need to "undo" +4 so
we subtract 4 from each side.
This gives us 3x = 6
Now, we need to "undo" 3 times
x, so we divide each side by 3
x = 2
Now, we have the solution
Check:
substitute 2 for x in the original equation
3 (2) + 4 = 10
6 + 4 = 10
10 = 10 (notice that it also required 2 steps to check)
Example 2
-2x - 6 = 12
This equation will require 2 steps to
solve it
-2x - 6 + 6 = 12 + 6
First, we need to "undo" -6 so
we add 6 to each side
This gives us -2x = 18
Now, we need to "undo" -2 times
x, so we divide each side by -2
x = -9
Now, we have the solution
Check: substitute -9 for x in the original equation
-2 (-9) -6 = 12
18 - 6 = 12
12 = 12
Example 3
This equation will require 2 steps to
solve it
First, we need to "undo" +9 so
we subtract 6 from each side
This gives us
Now, we need to "undo"
(which
is x divided by 4), so we multiply each each side by 4.
x = -12
Now, we have the solution
Check:
substitute -12 for x in the original equation
-3 + 9 = 6
6 = 6
Example 4
In this equation, keep in mind that the
expression 2-3x is being divided by 4
Since we're
dividing an entire expression by another number, we need
to deal with that first.
First, we need to "undo" the
divided by 4 so we multiply each side by 4
This will
eliminate the division and therefore simplify our
equation. Notice that on the right-hand side, the fours
cancel out each other
48 = 2-3x
After multiplying both sides by 4 we get
to this equation
48 -2 = 2-3x -2
Now, we need to "undo" the 2
(positive 2) so we subtract 2 from each side (Remember,
we are trying to isolate the variable - get the x by
itself, so we Need to get rid of the 2 first.) This will
give us 46 = -3x
To "undo" the -3 times x, we
divide each side by -3
This is the solution
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