Download Like Terms Combining Like Terms

Math 90
2.3 "Simplifying Expressions to Solve Equations"
Objectives:
*
Learn about like terms.
*
Combine like terms.
*
Solve equations.
*
Identify between identities and contradictions.
Like Terms
Recall that a term is either a number or the product of numbers and variables. For example
:
The number of each term is called the coe¢ cient. For example
:
Like Terms:
kLike terms, or similar terms, are terms with exactly the same variables and exponents.k
Example 1: (Identifying the like terms)
Identify the like terms in the following expressions.
a) 4x3 + 5x
4x2 + 2x3 + x2
b) 8x3 + 7x2
11
4x3
8x2
29
Combining Like Terms
The distributive property can be used to combine terms of algebraic expressions that contain sums or di¤erences of like
terms.
Combining Like Terms:
kTo combine like terms, add their coe¢ cients and keep the same variables and exponents.k
Example 2: (Combining or collecting like terms)
Simplify each expression.
a)
5 (x + 3) + 2 (x
c) 7 3x
2
7
5)
5 2x
b) 3y
3
5
+x
6 (y + z) + y
d) 6:7 (t
Page: 1
2:1) + 5:5 (t + 1)
Notes by Bibiana Lopez
Beginning and Intermediate Algebra by Gustafson and Frisk
2.3
Solving Equations
To solve an equation, we must isolate the variable on one side. As we solve equations we will follow these steps.
Solving Equations:
1: Clear the equation of fractions.
2: Use the distributive property to remove parentheses.
3: Combine like terms on each side of the equation, if necessary.
4: Undo the operations of addition and subtraction to get the variables on one side and the constants on the other.
5: Combine like terms and undo the operations of multiplication and division to isolate the variable.
6: Check the solution.
Example 3: (Solving equations)
Solve each equation and check the answer.
a)
c)
e)
2 (y
2x
3) = 4y
5
4
20
a
2
=x
=
2
3
(a + 4)
2
b) 4 (z + 3) =
d) 0:3 (20
f)
Page: 2
3 (z
4)
x) + 0:5x = 15
2 (2r 1)
3 (r + 7)
+5=
6
6
Notes by Bibiana Lopez
Beginning and Intermediate Algebra by Gustafson and Frisk
2.3
Identities and Contradictions
An equation that is true for all values of its variables is called an identity. An equation that is not true for any number
is called a contradiction.
Example 4: (Solving equations that are either identities or contradictions)
Solve each equation.
a)
2 (x + 3)
18x = 5 (9
c) 2 (s + 2) = 2 (s + 1) + 3
4x)
51
b) 5 (x
2)
d) x + 7 =
Page: 3
2x = 3 (x + 7)
2x + 6
+4
2
Notes by Bibiana Lopez