Name ____________________
3.4 – 3.6 Review Notes
3.4
Some equations will have variables on BOTH sides of the equation. To solve this type of
problem, you can collect the _________________ terms on one side of the equation and the
________________ terms on the other side. It does not matter which side each is on.
Example 1:
Example 2:
7 – 8x = 4x – 17
9x – 5 = 4x + 15
*Sometimes you have to _______________
first before you move terms to the other
side!
Example 3: 19 + c = ½(8c + 14)
Example 4: When there are multiple variables on one side of the equation, you can
combine those first, then move the terms to the other side as “one.”
2 + 4x – 6 = 2x + 6 – 3x
Guided Practice:
1. 24 – 3m = 5m
2. 9 – 3k = 17 – 2k
3. 5z – 2 = 2(3z – 4)
4. 7w + 1 = 8w + 1
5. 10x = 2x + 9 – x
6. 24y = -24
Some equations have one solution (like the ones we’ve seen), some equations have no
solution, where NO number would work for the variable, and some equations are an
identity, where any number would work for the variable. Here are some examples:
One Solution
No Solution
Identity
1.) 5x – 8 = 2x – 2
2.) 4 + 2c = 2(c + 3)
3.) 10 + 3x = x + 10 + 2x
7. 22x + 70 = 17x – 95
8. 2 – 15n = 5(-3n + 2)
9. 12y + 6 = 6(2y + 1)
3.5
Proportions
A proportion is an ______________ that states that two ratios are ________________. The
general form of a proportion is:
a c
=
where b  0, d  0
b d
This proportion is read “a is to b as ________________”
Examples
Solve the proportion and check your solution.
1)
2 x

3 9
5)
6
7
=
2)
12
𝑥
6)
4
5
2
5
=
=
𝑥
3)
25
6
7)
𝑥
x 3

12 4
𝑥
10
=
3
30
4)
8) )
x 1

24 8
𝑥
4
=
12
16
3.6
Solve each proportion using cross-products. (NOTE – Sometimes you have to distribute!)
1)
4 12

a 24
2)
3
9

x x4
3)
4
8

x x3
Guided Practice:
Solve the proportion. Check your solutions.
3.)
4
24
=
a
30
4.)
3
2
=
x
x6
5.)
m
m6
=
5
4
6.)
x 12
=
6 24