Download Distributive Property and Equations


Algebra 1 Part 2 - Solving Equations
Name___________________________________
Distributive Property and Equations
Date________________
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1) DIRECTIONS: You will now be solving more complicated equations that have parentheses in them.
Step1) If you see parentheses apply the distributive property
...BE CAREFUL OF A SUBTRACTION SIGN THAT IS IN IN FRONT OF A NUMBER NEXT TO A
PARENTHESES. YOU MUST TREAT THE SUBTRACTION SIGN AS IF IT WERE A NEGATIVE
NUMBER.
See the subtraction sign in front of the 3 below:
5x - 3(2x+5) = 7(2x + 1) - 6
5x - 6x - 15 = 14x + 7 - 6
Step 2) Add or subtract any like terms that may be on the same side of the equation.
5x - 6x - 15 = 14x + 7 - 6
-1x - 15 = 14x + 1
Step 3) Now you will have an equation that resembles those you have solved in the past.
-1x - 15 = 14x + 1
-1x - 14x = 1 + 15
-15x
= 16
-15x/15 = 16/-15
x = - 16/15
TEACHER COMMENT:
...If ALL your variables vanish and you end up with a TRUE EQUATION then your answer is ALL REAL
NUMBERS.
...If ALL your variables vanish and you end up with a FALSE EQUATION then your answer is NO
SOLUTION.
Solve each equation.
2) n(n)
A)
B)
C)
D)


3) (a)a
A) 
C) No solution.
B) 
D) 
{ All real numbers. }
No solution.
4)  x( x) x
A) 
C) 
B) 
D) 
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5) (v)v
A) 
C) 
-1-
B) 
D) 
Worksheet by Kuta Software LLC

6)  x( x) x
A) 
C) 
B) 
D) 
8) (n)n
A) 
C) 
B) 
D) 
B) 
D) No solution.
12) m(m)m
A)
B)
C)
D)


{ All real numbers. }

14)  x( x)
A) 
C) No solution.
B) 
D) 
B) 
D) 
18) (v)v
A) 
C) 
B) 
D) 
20) aa(a)
A) 
C) 
B) 
D) No solution.
22) (k)k
A) 
C) 
B) 
D) 
A) 
C) 
B) 
D) 
11) n(n)
A) 
C) 
B) 
D) 
13) r(r)
A)
B)
C)
D)


No solution.
{ All real numbers. }
15)  p( p)
16) (n)n
A) 
C) 
A) 
C) 
9) kk(k)
10) ( x) x
A) 
C) 
7) ( x) x
B) 
D) 
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A) 
C) 
B) 
D) 
17) (b)b
A) 
C) 
B) 
D) 
19) ( x) x
A) 
C) 
B) 
D) 
21) (n)n
A) 
C) 
B) 
D) 
23) ( x) x
A)
B)
C)
D)
-2-



{ All real numbers. }
Worksheet by Kuta Software LLC

24) n(n)
A) 
C) 
B) 
D) 
26) (r)r
A) 
C) 
28)  x x( x)
B) 
D) 
30) (n)n
A) 
C) 
B) 
D) 
B) 
D) 
34)  x( x)
A) 
C) 
B) 
D) No solution.
36)  x( x) x
A) 
C) 
B) 
D) 
38) (n)n
A) No solution.
C) 
B) 
D) 
A) 
C) 
B) 
D) 
29) (b)b
A) 
C) 
B) 
D) 
31) (v)v
32) (n)n
A) 
C) 
A) 
C) 
27) (m)m
B) 
D) 
A) 
C) 
25) ( p) p
B) 
D) 
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A) 
C) 
B) 
D) 
33) (a)a
A)
B)
C)
D)



{ All real numbers. }
35) vv(v)
A) 
C) 
B) 
D) 
37) ( x) x
A)
B)
C)
D)
{ All real numbers. }

No solution.

39)  p( p) p
A)
B)
C)
D)
-3-


{ All real numbers. }

Worksheet by Kuta Software LLC

40) (k)k
A) No solution.
C) 
B) 
D) 
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41)  x( x)
A)
B)
C)
D)
-4-

{ All real numbers. }


Worksheet by Kuta Software LLC
Answers to Distributive Property and Equations
1) The dot next to the choice indicates that it is the answer.
2) C
3) B
4) C
6) A
7) C
8) B
10) B
11) C
12) A
14) B
15) A
16) C
18) B
19) D
20) D
22) D
23) B
24) A
26) B
27) B
28) A
30) C
31) C
32) B
34) A
35) D
36) B
38) B
39) A
40) D
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-5-
5) A
9) A
13) B
17) A
21) B
25) D
29) C
33) D
37) B
41) D
Worksheet by Kuta Software LLC