Transcript 11-1 Simplifying Algebraic Expressions Warm Up Problem of the Day

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.
Like terms can be grouped together
because they have the same variable raised
to the same power.
Helpful Hint
Equivalent
expressions
same
Constants such
as 4, 0.75,have
and the
11 are
like
value
all values
ofof
the
variables.
termsfor
because
none
them
have a 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
To simplify an expression, perform all
possible operations, including
combining like terms.
Remember!
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 + n) – 2n
6(5) + 6(n) – 2n
Distributive Property.
30 + 6n – 2n
Multiply.
30 + 4n
Combine coefficients 6 – 2 = 4.
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
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