Question

|2t| - 5 = 7

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we'll isolate the absolute value by adding 5 to both sides:

|2t| = 7 + 5
|2t| = 12

Now, consider two cases:
Case 1: 2t = 12
If we remove the absolute value signs, we get 2t = 12. To solve for t, divide both sides by 2:
2t/2 = 12/2
t = 6

Case 2: -2t = 12
If we remove the absolute value signs and change the sign, we get -2t = 12. To solve for t, divide both sides by -2:
-2t/-2 = 12/-2
t = -6

Therefore, the solutions are t = 6 and t = -6.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation |2t| - 5 = 7, we will follow these steps:

Step 1: Add 5 to both sides of the equation.
|2t| - 5 + 5 = 7 + 5

This simplifies to:
|2t| = 12

Step 2: Split the equation into two cases:

Case 1: 2t is positive.
If 2t is positive, then the equation becomes:
2t = 12

Step 3: Divide both sides of the equation by 2.
(2t) / 2 = 12 / 2

This simplifies to:
t = 6

Case 2: 2t is negative.
If 2t is negative, then the equation becomes:
-2t = 12

Step 3: Divide both sides of the equation by -2.
(-2t) / -2 = 12 / -2

This simplifies to:
t = -6

Thus, the solutions to the equation |2t| - 5 = 7 are t = 6 and t = -6.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation |2t| - 5 = 7, we can follow these steps:

Step 1: Isolate the absolute value expression.
We begin by adding 5 to both sides of the equation to move the constant term to the right side:
|2t| = 7 + 5
Simplifying, we have:
|2t| = 12

Step 2: Express the absolute value as two separate cases.
The absolute value expression |2t| can be either positive or negative. Thus, we split the equation into two separate cases and solve each one.

Case 1: 2t is positive
In this case, |2t| can be expressed as 2t. Substituting this into the equation gives us:
2t = 12

Case 2: 2t is negative
In this case, |2t| can be expressed as -2t. Substituting this into the equation gives us:
-2t = 12

Step 3: Solve each case separately.
We'll solve both cases and find the value of t in each.

Case 1: 2t = 12
We divide both sides of the equation by 2 to isolate t:
2t/2 = 12/2
t = 6

Case 2: -2t = 12
Similarly, divide both sides of the equation by -2:
-2t/-2 = 12/-2
t = -6

Step 4: Check the solutions.
We need to check whether our solutions, t = 6 and t = -6, satisfy the original equation:
|2(6)| - 5 = 7
|12| - 5 = 7
12 - 5 = 7
7 = 7

|2(-6)| - 5 = 7
|-12| - 5 = 7
12 - 5 = 7
7 = 7

Both solutions, t = 6 and t = -6, satisfy the equation, so they are both valid solutions.