Question

Caleb solved the equation 3x + 12 + x = 8 + 4 + x by following the steps shown below.

Step 1: 4x + 12 = 12 + x
Step 2: 3x + 12 = 12
Step 3: 3x = 0
Step 4: x = 0

Select FOUR statements that correctly describe the steps of Caleb's work.
*
4 points
Caleb applied the distributive property going from the given equation to step 1.
Caleb combined like terms going from the given equation to step 1.
Caleb applied the Subtraction Property of Equality going from step 1 to step 2.
Caleb applied the Addition Property of Equality going from step 1 to step 2.
Caleb made an error going from step 2 to step 3. He should have gotten the equation 3x = 24 in step 3.
Caleb applied the Subtraction Property of Equality going from step 2 to step 3.
Caleb applied the Multiplication Property of Equality going from step 3 to step 4.
Caleb applied the Division Property of Equality going from step 3 to step 4.
If Caleb hadn't made a mistake on step 3, he would have applied the Division Property of Equality and arrived at a solution of x = 8.
Select the answer choice that best describes the solution to the equation shown below.

4(x + 1) = 4x + 1
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1 point
x = 1
x = 4
No Solutions
Infinitely Many Solutions

Answer 1

Four correct statements:
- Caleb combined like terms going from the given equation to step 1.
- Caleb applied the Subtraction Property of Equality going from step 1 to step 2.
- Caleb applied the Subtraction Property of Equality going from step 2 to step 3.
- Caleb applied the Division Property of Equality going from step 3 to step 4.

Second question:
- No Solutions (because 4(x+1)=4x+4 gives 4x+4 = 4x+1 → 4 = 1, a contradiction).