The document provides step-by-step explanations and examples of solving different types of one-variable equations. It demonstrates isolating the variable by adding or subtracting the same quantity to both sides of the equation, dividing or multiplying both sides by the same non-zero quantity, and using these techniques to solve equations such as 3x + 7 = 4, 2x = 5, 4x = 8, and x/2 = 3.

2. Both sides must remain equal, so if you
change one side of the balance, you must
change the other in the same way!
=

3. x
=- x
=
=
=
1
-1
These work the same way the
pictures (and candy!) work.

4. x 3 7
=
We need to
isolate the
variable (x)…

5. x 3 7
x 3
3
7
3
x
4
…which means we need to
take away 3 from both sides…
=
…so we are left with x = 4.

6. x 2 5
=
We need to
isolate the
variable (x)…
…but there are
no negatives
to take away…

7. x 2 5
=
…so we need to
make zero pairs…
…by adding two
positives to both
sides…

8. x 2 5
x 2
2
5
2
x
7
=
…which allows us to
cancel the -2 on the
left, but leaves us
with x = 7.

9. 4x 8
=
We need to
isolate one of the
variables (x)…

10. 4x 8
=
…which means we
need to split both
sides into equal
groups…

11. 4x 8
4x 8
4 4
x 2
=
…so we are
left with x = 2.

12. 2x
=
We need to
isolate one of the
variables (x)…
4

13. 2x
=
4
…which means we
need to split both
sides into equal
groups…

14. 2x
2x
2
x
4
2
2
4
=
…so we are left
with -x = 2…

15. 2x
2x
2
x
4
2
2
4
=
…but we need x not - x
so we take the opposite
of both sides x = -2.

16. x
2
3
=
We want to know what
one whole variable
equals…
…but we only have half…

17. x
2
x
2
2
x
32
6
3
=
…so we need to double
what we have on both
sides, leaving x = -6.