Question

2(x + 7) + 3x = 12

What is the first step in solving this equation for x?
Responses
A 2x + 14 + 3x = 12
B 2x + 7 + 3x = 12
C 2x + 14 = 9
D 5x = -2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The first step in solving this equation for x is to distribute the 2 to both terms inside the parentheses. So, the correct answer is:

A) 2x + 14 + 3x = 12

Answer 2

Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36

Given ⇒ 3(x − 4) + 5x = 9x − 36
Step 1 ⇒ 3x − 12 + 5x = 9x − 36
Step 2 ⇒ 3x + 5x − 12 = 9x − 36
Step 3 ⇒ 8x − 12 = 9x − 36
Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36
Step 5 ⇒ 0 − 12 = x − 36
Step 6 ⇒ −12 = x − 36
Step 7 ⇒ −12 + 36 = x − 36 + 36
Step 8 ⇒ 24 = x + 0
Step 9 ⇒ 24 = x

Which property yields Step 4?
Responses
A Subtraction Property of Equality
B Commutative Property of Addition
C Addition Property of Equality
D Additive Inverse Property

Answer 3

[AI-generated answer — Bot GPT 3.5]

The property that yields Step 4 is:

A) Subtraction Property of Equality

Answer 4

Given that x + y = 180, p + q = 180, and p = x. Show that y = q.

Which step would be used to prove the argument?
Responses
A x + p = 180
B x + y = p + q
C y + q = 180
D 2x + 2y = 180

Answer 5

[AI-generated answer — Bot GPT 3.5]

The step that would be used to prove the argument is:

B) x + y = p + q

Answer 6

Consider the sequence of steps to solve the equation:

5(x - 3) = 7x/2

Step 1 ⇒ 10(x - 3) = 7x
Step 2 ⇒ 10x - 30 = 7x
Step 3 ⇒ 3x - 30 = 0
Step 4 ⇒ 3x = 30
Step 5 ⇒ x = 10

Identify the property of equality which gets us from Step 3 to Step 4.
Responses
A Division Property
B Addition Property
C Subtraction Property
D Multiplication Property

Answer 7

[AI-generated answer — Bot GPT 3.5]

The property of equality that gets us from Step 3 to Step 4 is:

D) Multiplication Property

Answer 8

4x + 5x + 12 = -6 (given)

9x + 12 = -6 (simplify)
9x = -18 (subtraction)
x = -2 (addition)

Which reason is incorrect?
Responses
A addition
addition
B given
given
C simplify
simplify
D subtraction

Answer 9

[AI-generated answer — Bot GPT 3.5]

The reason that is incorrect is:

C) simplify

Step 2, where 4x + 5x is simplified to 9x, is incorrect. It should actually be simplified to 9x + 12, not just 9x.

Answer 10

How many solutions does this equation have?

2+6x/2 = 3x + 3
Responses
A no solutionno solution
B exactly one solutionexactly one solution
C exactly two solutionsexactly two solutions
D infinitely many solutions

Answer 11

[AI-generated answer — Bot GPT 3.5]

The equation has:

B) exactly one solution.