This document is a lesson on simplifying algebraic expressions. It contains examples of combining like terms, using the distributive property, and solving equations. Key steps include identifying like terms, combining coefficients, distributing terms, and solving equations by isolating the variable. The lesson teaches students to simplify expressions by performing all possible combinations of like terms.

1. 11-1 Simplifying Algebraic Expressions
Course 3
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation

2. Warm Up
Simplify.
20
11
8
3
Course 3
11-1 Simplifying Algebraic Expressions
4. 17 + 8 − 20 − 2
3. 6 + 9 − 10 + 3
2. 16 − 8 + 4 − 1
1. 9 + 13 − 5 + 3

3. Problem of the Day
Ray and Katrina are wandering through
the wildlife preserve. They observe and
count a total of 15 wild turkeys and deer
and a total of 46 legs. How many of each
did they see? 7 turkeys, 8 deer
11-1 Simplifying Algebraic Expressions

4. Learn to combine like terms in an expression.
11-1 Simplifying Algebraic Expressions

5. Vocabulary
term
like term
equivalent expression
simplify
11-1 Simplifying Algebraic Expressions

6. Terms in an expression are separated by
plus or minus signs.
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.
11-1 Simplifying Algebraic Expressions
Constants such as 4, 0.75, and 11 are like
terms because none of them have a variable.
Helpful Hint

7. Combine like terms.
Additional Example 1: Combining Like Terms To
Simplify
Identify like terms.
Combine coefficients: 14 – 5 = 9
A. 14a – 5a
9a
B. 7y + 8 – 3y – 1 + y
Identify like terms ; the
coefficient of y is 1, because
1y = y.
Combine coefficients: 7 – 3 + 1 = 5
and 8 – 1 = 7
5y + 7
11-1 Simplifying Algebraic Expressions

8. Combine like terms.
Additional Example 2A: Combining Like Terms in
Two-Variables Expressions
Identify like terms.
Combine coefficients: 9 – 2 = 7
9x + 3y – 2x + 5
7x + 3y + 5
9x + 3y – 2x + 5
11-1 Simplifying Algebraic Expressions

9. Combine like terms.
Additional Example 2B: Combining Like Terms in
Two-Variable Expressions
Identify like terms.
Combine coefficients: 5 – 2 = 3
and 7 – 3= 4
5t + 7p – 3p – 2t
3t + 4p
5t + 7p – 3p – 2t
11-1 Simplifying Algebraic Expressions

10. Combine like terms.
Additional Example 2C: Combining Like Terms in
Two-Variable Expressions
No like terms.
4m + 9n – 2
4m + 9n – 2
11-1 Simplifying Algebraic Expressions

11. To simplify an expression, perform all
possible operations, including
combining like terms.
11-1 Simplifying Algebraic Expressions
The Distributive Property states that a(b + c)
= ab + ac for all real numbers a, b, and c. For
example, 2(3 + 5) = 2(3) + 2(5).
Remember!

12. Simplify 6(5 + n) – 2n.
Additional Example 3: Using the Distributive Property
to Simplify
Distributive Property.
Multiply.
6(5 + n) – 2n
30 + 6n – 2n
6(5) + 6(n) – 2n
30 + 4n Combine coefficients 6 – 2 = 4.
11-1 Simplifying Algebraic Expressions

13. Solve x + 3x = 48.
Additional Example 4: Combining Like Terms to Solve
Algebraic Equations
Identify like terms. The coefficient of x is 1.
Combine coefficients: 1 + 3 = 4
x + 3x = 48
4x = 48
4x = 48
x = 12
Divide both sides by 4.
4 4
11-1 Simplifying Algebraic Expressions

14. Lesson Quiz
Combine like terms.
1. 3x + 4 + 2x 2. 13k + 6 − 8m + 9 + k
Simplify.
3. 4(3x + 6) − 7x 4. 6(x + 5) + 3x
Solve.
5. 6y + y = 42
6. The accounting department ordered 15 boxes of
pens. The marketing department ordered 9 boxes of
pens. If the total cost of the combined order was $72,
what is the price of each box of pens?
14k – 8m + 15
y = 6
5x + 4
5x + 24 9x + 30
$3
11-1 Simplifying Algebraic Expressions