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Solving Linear Equations: Distributive Property Answers

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Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four”?

A
(1 – n) – 3 = (4 – 3n)
Option A
B
3 – (1 – n) = (4 – 3n)
Option B
C
(n – 1) – 3 = (3n – 4)
Option C
D
3 – (n – 1) = (3n – 4)
Option D
2
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How many solutions exist for the given equation?3(x – 2) = 22 – x

A
zero
B
one
C
two
D
infinitely many
3

Which equation has no solution?

A
4(x + 3) + 2x = 6(x + 2)
B
5 + 2(3 + 2x) = x + 3(x + 1)
C
5(x + 3) + x = 4(x + 3) + 3
D
4 + 6(2 + x) = 2(3x + 8)
4

How many solutions exist for the given equation?0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)

A
zero
B
one
C
two
D
infinitely many
5

Karissa begins to solve the equation . Her work is correct and is shown below.

Question illustration
A
–1
B
–
Option B
C
0
D
StartFraction one-half EndFraction.
Option D
6

Solve for n.11(n – 1) + 35 = 3n

A
n = –6
B
n = –3
C
n = 3
D
n = 6
7

What is the value of x in the equation 2(x−3)+9=3(x+1)+x?

A
x = −3
B
x = −1
C
x = 0
D
x = 3
8

How many solutions exist for the given equation?(x + 12) = 4x – 1

Question illustration
A
zero
B
one
C
two
D
infinitely many
9

How many solutions exist for the given equation?3x + 13 = 3(x + 6) + 1

A
zero
B
one
C
two
D
infinitely many
10

What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?

A
3
B
4
C
5
D
9

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