Download HOLT 11-1 Simplifying Algebraic Expressions

11-1 Simplifying Algebraic Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course 3
11-1 Simplifying Algebraic Expressions
Warm Up
Simplify.
1.
2.
3.
4.
Course 3
9 + 13  5 + 3 20
16  8 + 4  1 11
6 + 9  10 + 3 8
17 + 8  20  2 3
11-1 Simplifying Algebraic Expressions
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
Learn to combine like terms in an expression.
11-1 Simplifying Algebraic Expressions
Vocabulary
term
like term
equivalent expression
simplify
11-1 Simplifying Algebraic Expressions
Terms in an expression are separated by plus or
minus signs.
Variable: A letter used to represent a mystery
number.
Like terms can be grouped together because they
have the same variable raised to the same power.
Constant: A number without a variable. All constants
can be combined because they are like terms.
Coefficient: The number in front of a variable. This
number is being multiplied by the variable.
11-1 Simplifying Algebraic Expressions
Additional Example 1: Combining Like Terms To
Simplify
Combine like terms.
A. 14a – 5a
9a
Identify like terms.
B. 7y + 8 – 3y – 1 + y
Identify like terms ; the
coefficient of y is 1, because
1y = y.
5y + 7
Combine coefficients: 14 – 5 = 9
Combine coefficients: 7 – 3 + 1 = 5
and 8 – 1 = 7
11-1 Simplifying Algebraic Expressions
Additional Example 2A: Combining Like Terms in
Two-Variables Expressions
Combine like terms.
9x + 3y – 2x + 5
9x + 3y – 2x + 5
Identify like terms.
7x + 3y + 5
Combine coefficients: 9 – 2 = 7
11-1 Simplifying Algebraic Expressions
Additional Example 2B: Combining Like Terms in
Two-Variable Expressions
Combine like terms.
5t + 7p – 3p – 2t
5t + 7p – 3p – 2t
Identify like terms.
3t + 4p
Combine coefficients: 5 – 2 = 3
and 7 – 3= 4
11-1 Simplifying Algebraic Expressions
Additional Example 2C: Combining Like Terms in
Two-Variable Expressions
Combine like terms.
4m + 9n – 2
4m + 9n – 2
No 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).
11-1 Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive Property
to Simplify
Simplify 6(5 + n) – 2n.
6(5) + 6(n) – 2n Distributive Property.
30 + 6n – 2n
Multiply.
30 + 4n
Combine like terms.
6 – 2 = 4.
11-1 Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive Property
to Simplify
Simplify 5(3 + 2n) – n.
5(3) + 5(2n) – n Distributive Property.
15 + 10n – n
Multiply.
15 + 9n
Combine like terms
11-1 Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive Property
to Simplify
Simplify 5(6 – 5x) + 10.
5(6) - 5(5x) + 10
Distributive Property.
30 – 25x + 10
Multiply.
40 – 25x
Combine like terms
11-1 Simplifying Algebraic Expressions
Check It Out: Example 3
Simplify 3(c + 7) – c.
3(c) + 3(7) – c
Distributive Property.
3c + 21 – c
Multiply.
2c + 21
Combine like terms
3 – 1 = 2.
11-1 Simplifying Algebraic Expressions
Additional Example 4: Combining Like Terms to Solve
Algebraic Equations
Solve x + 3x = 48.
x + 3x = 48
Identify like terms. The coefficient of x is 1.
4x = 48
Combine coefficients: 1 + 3 = 4
4x = 48
4
4
Divide both sides by 4.
x = 12
11-1 Simplifying Algebraic Expressions
Check It Out: Example 4
Solve 7c – c = 102.
7c – c = 102
Identify like terms. The coefficient of c is 1.
6c = 102
Combine coefficients: 7 – 1 = 6
6c = 102
6
6
Divide both sides by 6.
c = 17
11-1 Simplifying Algebraic Expressions
Lesson Quiz
Combine like terms.
1. 3x + 4 + 2x 5x + 4
Simplify.
2. 13k + 6  8m + 9 + k
14k – 8m + 15
3. 4(3x + 6)  7x 5x + 24 4. 6(x + 5) + 3x 9x + 30
Solve.
5. 6y + y = 42 y = 6
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? $3