Download (Class worksheet) Simplifying Expressions and solving linear

Simplifying Expressions
Name _____________________________
Rule Number 1. Only combine like terms.
Examples:
1.
2 apples plus 3 apples equals 5 apples.
2.
2 x  3x  5x
3.
2 x  3x   x
4.
3x  5x  4 x  2 x
5.
2 x  3 y  3x  y  5x  4 y
Always pay attention to the sign in FRONT of the term. Try these:
6.
2 x  5x 
7.
2 x  3x 
8.
2 x  3 y  5x  y 
9.
2a  3b  5a  6b 
Rule Number 2. Multiplication distributes over addition and subtraction. This is
how parentheses are eliminated.
10.
Sara had two apples and three pears. Jan has three times as much of each fruit. Jan has
____ apples and ____ pears.
11.
3 (2a  3 p ) =
12.
3 (2a  3 p ) =
13.
 3 (2a  3 p ) =
14.
 3 (2a  3 p ) =
Simplify each expression using these rules.
15.
2 ( x  3) 
16.
2 ( x  3)  3 ( x  2) 
17.
2 (3x  1)  3 ( x  5) 
18.
2 (3x  1)  3 x  5 
19.
2 [ (3x  1)  3 ( x  5)] 
20.
2 (3 x  1)  3( x  5) 
Equations-1
The solution set for an equation is the set of all numbers that when used in placed of the
variable make the equation true.
Find the solution set for each equation:
Solution:
1.
x2  3
{5}
2.
x2  x3
There is not solution.
3.
2( x  3)  2 x  6
the set of all real numbers
4.
x35
_____________________
5.
2x  6
_____________________
6.
3x  12
_____________________
7.
2 x 5
_____________________
8.
2( x  3)  2 x  3
_____________________
9.
2x  1  9
_____________________
10.
x2  2 x
_____________________
Sometimes an equation has to be rewritten before it is easy to find the solution set. In
general, your first step will be to simplify each side of the equation. Remember that
means getting rid of parentheses (distributive rule) and combining like terms.
Find the solution set for each of theses equations:
Solution set:
11.
2( x  3)  5  x  3
_____________________
12.
2( x  2)  x  5
_____________________
13.
3( x  2)  2( x  2)  5
_____________________