Transcript Like Terms

Algebraic Expressions
Warm Up
Change 0.483 to a Percent
48.3%
Simplify
Simplify
x
18
1
18
x
32
16 2
4 2
Like Terms

Term- a number, variable, or product of a
number and one or more variables


Like Terms- terms with the same variables
and the same exponents


Ex.: 3a – 4b + 5 has 3 terms
Ex.: 2x, 3x
4mn, 12mn
In the term 3a, 3 is called
the numerical coefficient
Note:
x and x 2
are
NOT like terms
Simplify
 9b  4b
4 p  6  8 p  17
 5b
 4 p  8 p  6  17
 4 p  11
Simplify
 8m  3m
 5x  13x
 5m
 18x
Simplify
2 p  7  9 p  19
 2 p  9 p  7  19
 7 p  12
 46  x   x  5  6x
 24  4 x  x  5  6 x
 4 x  x  6 x  24  5
  x  29
Solving Equations
Solving Equations

In this section we are going to learn how to solve
linear (or first degree) equations.

A linear equation is one in which the exponent
on the variable is 1.

Example: 5x – 1 = 3
2x + 4 = 6x - 5
Equivalent Equations


Equivalent Equations are equations that
have the same solution.
The following are equivalent equations:
2x – 5 = 1
2x = 6
x=3

When we solve an equation, we write the
equation as a series of simpler equivalent
equations until we obtain an equation of the
form x = c, where c is some real number.
Isolate the Variable



To solve any equation, we have to isolate
the variable.
That means getting the variable by itself on
one side of the equals sign.
There are 4 properties we will use to isolate
the variable.
Addition Property of Equality
You can add the same number to both
sides of an equation and the equation
remains equivalent.
Example: Solve x  9  15
x  9  9  15  9
x  0  24
x  24
Subtraction Property of
Equality
You can subtract the same number to both
sides of an equation and the equation
remains equivalent.
Example: Solve x  11  19
x  11  11  19  11
x09
x 8
Multiplication Property of
Equality
You can multiply the same number on both
sides of an equation and the equation
remains equivalent.
x
Example: Solve
3
6
x
6  3 6
6
x  18
Division Property of Equality
You can divide the same number on both
sides of an equation and the equation
remains equivalent.
Example:
Solve 4 x  28
4 x 28

4
4
x7
Procedure to Solve Equations
1. Get rid of fractions.
2. Distribute when needed.
3. Combine like terms on same side of equals.
4. Use the addition/subtraction property. You
may have to use it more than once!
5. Solve using either the multiplication property
or the division property.
Solve
4 x  2  82
4 x  2  2  82  2
4 x  80
4 x 80

4
4
x  20
2 x  5  65
2 x  5  5  65  5
2 x  60
2 x 60

2
2
x  30
Solve
5a  7  38
 18  3 y  12
5a  7  7  38  7
 18  18  3 y  12  18
5a  45
 3y  6
 3y
6

3 3
y  2
5a 45

5
5
a9
Solve
4  13  7a  8a
3a  4a  7  11
4  13  7 a  8a
 a  7  11
4  13  a
4  13  13  13  a
17   a
 a  7  7  11  7
a4
17  a

1 1
 17  a
a
4

1 1
a  4
Variables on Both Sides

Your goal is to get the variable on one side of
the equals sign and everything else on the
other side of the equals sign.

Always combine like terms on each side of
the equation FIRST!
Example:
4x  5  x  8
4x  5  x  x  x  8
3x  5  8
3x  5  5  8  5
3x  13
3x  13

3
3
13
x
3
Solve
4x  3  x  12
3x  2x  4
4 x  x  3  x  x  12
3 x  3  12
3 x  3  3  12  3
3x  9
3x 9

3 3
x3
3x  2 x  2 x  2 x  4
x4
Solve
2x  4  3x  x  8
7  x  10  9x
5x  4  x  8
5x  x  4  x  x  8
7  10 x  10
4x  4  8
4x  4  4  8  4
4x  4
4x 4

4 4
x 1
17  10 x
17 10 x

10 10
17
x
10
7  10  10 x  10  10
Grouping Symbols
You have to distribute before
you combine like terms.
Solve
2x  3  x  7
2x  6  x  7
2x  x  6  x  x  7
x67
x6676
x 1
22 x  3  18
4 x  6  18
4 x  6  6  18  6
4 x  12
4 x 12

4
4
x3
Solve
5  3x  4  11
5  3 x  12  11
5  3x  1
5  1  3x  1  1
6  3x
6 3x

3 3
2x
20  3x  2x  1  7 x
20  3x  2 x  2  7 x
20  3x  5 x  2
20  3x  5 x  5 x  5 x  2
20  2 x  2
20  20  2 x  2  20
2 x  18
2x
18

2
2
x  9