Vocabulary
Simplify expressions by combining like
terms and using the distributive property.
term
like term
equivalent expression
simplify
Terms in an expression are separated by
plus or minus signs.
Combing Like Terms
Like terms can be grouped together
because they have the same variable raised
to the same power.
Equivalent expressions have the same
value for all values of the variables.
1
Additional Example 1: Combining Like Terms To
Simplify
Combine like terms.
A. 14a – 5a
9a
B. 7y + 8 – 3y – 1 + y
5y + 7
Additional Example 2A: Combining Like Terms in
Two-Variables Expressions
Combine like terms.
A. 9x + 3y – 2x + 5
9x + 3y – 2x + 5
7x + 3y + 5
Identify like terms.
Combine coefficients: 14 – 5 = 9
Identify like terms ; the
coefficient of y is 1, because
1y = y.
Combine coefficients: 7 – 3 + 1 = 5
and 8 – 1 = 7
Additional Example 2B: Combining Like Terms in
Two-Variable Expressions
Combine like terms.
B. 5t + 7p – 3p – 2t
Identify like terms.
Combine coefficients: 9 – 2 = 7
5t + 7p – 3p – 2t
3t + 4p
Identify like terms.
Combine coefficients: 5 – 2 = 3
and 7 – 3= 4
2
Additional Example 2C: Combining Like Terms in
Two-Variable Expressions
Combine like terms.
Combine like terms.
A. 4q – q
C. 4m + 9n – 2
4m + 9n – 2
Try This: Example 1
No like terms.
3q
B. 5c + 8 – 4c – 2 – c
6
Identify like terms; the
coefficient of q is 1, because
1q = q.
Combine coefficients: 4 – 1 = 3
Identify like terms; the
coefficient of c is 1, because
1c = c.
Combine coefficients: 5 – 4 – 1 = 0
and 8 – 2 = 6
Try This: Example 2
Combine like terms.
A. 2x + 5x – 4y + 3
2x + 5x – 4y + 3
Identify like terms.
7x – 4y + 3
Combine coefficients: 2 + 5 = 7
B. 9d + 7c – 4d – 2c
9d + 7c – 4d – 2c
Identify like terms.
5d + 5c
Combine coefficients: 9 – 4 = 5
and 7 – 2 = 5
C. 8g + c – 6
8g + c – 6
No like terms.
3
Solving Multi-Step Equations
1. Combine Like Terms (simplify)
2. Add or Subtract
3. Multiply or Divide
Additional Example 1: Solving Equations That
Contain Like Terms
Solve 12 – 7b + 10b = 18.
12 – 7b + 10b = 18
12 + 3b = 18
– 12
– 12
3b = 6
3b = 6
3
3
b =
2
Combine like terms.
Subtract 12 from both sides.
Divide both sides by 3.
Try This: Example 1
Solve 14 – 8b + 12b = 62.
14 – 8b + 12b = 62
14 + 4b = 62
– 14
– 14
4b = 48
4b = 48
4
4
b =
Combine like terms.
Subtract 14 from both sides.
Divide both sides by 4.
12
4
Sometimes one side of an equation has
has a variable expression as the
numerator of a fraction. With this type
of equation, it may help to first multiply
both sides of the equation by the
denominator.
Additional Example 2: Solving Equations That
Contain Fractions
Solve 3y – 6 = 3.
7
(7) 3y – 6 = (7)3
Multiply both sides by 7.
7
3y – 6 = 21
+6 +6
Add 6 to both sides.
3y
3y
3
= 27
= 27
3
y=9
Divide both sides by 3.
Whiteboard Practice
Try This: Example 2
4y – 4
= 14.
8
(8) 4y – 4 = (8)14 Multiply both sides by 8.
8
4y – 4 = 112
+4 +4
Add 4 to both sides.
Solve
4y
4y
4
= 116
= 116
4
y = 29
Divide both sides by 4.
Directions: Solve each equation by showing which
property you use and check your answer.
1.
2.
3.
4.
5.
6.
7.
8.
x=2
15x-8 – 3x = 16
5n + 3 + 4n = 30 n = 3
c=6
c – 6 +7c = 42
-3g + 6 + 2g = 15 g = -9
b=1
-2b + 7 – 3b = 2
5y + 1 + 3y = -15 y = -2
4k – 14 + 3k = 21 k = 5
m=3
9m + 10 – 14m = -5
5