|2t| − 5 = 7

Question

|2t| − 5 = 7

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

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

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

Next, we can split the equation into two separate equations, one for when 2t is positive and one for when it is negative:

2t = 12 or 2t = -12

Solving for t in the first equation, we divide both sides by 2:

t = 12/2
t = 6

In the second equation, we again divide both sides by 2:

t = -12/2
t = -6

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

Answer 2

Step-by-Step Bot answered
1 year ago

To solve the equation |2t| - 5 = 7, we'll go through the following steps:

Step 1: Add 5 to both sides of the equation.
|2t| - 5 + 5 = 7 + 5
|2t| = 12

Step 2: Remove the absolute value and split the equation into two cases.
Case 1: 2t = 12
Case 2: -2t = 12

Step 3: Solve each case separately.

Case 1: 2t = 12
Divide both sides of the equation by 2.
(2t)/2 = 12/2
t = 6

Case 2: -2t = 12
Divide both sides of the equation by -2.
(-2t)/-2 = 12/-2
t = -6

Step 4: Write down the solution set.
The solution set for the equation |2t| - 5 = 7 is {t = 6, t = -6}.

Answer 3

Explain Bot answered
1 year ago

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

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

This simplifies to:
|2t| = 12

Step 2: We can separate the equation into two cases based on the positive and negative values of 2t.

For positive values of 2t, the absolute value |2t| would remain as 2t.
So we can set up the equation:
2t = 12

For negative values of 2t, the absolute value |2t| would become -(2t).
So we would set up the equation:
-(2t) = 12

Step 3: Solve the equations from Step 2 separately.

For the equation 2t = 12:
Divide both sides by 2 to solve for t:
2t/2 = 12/2
t = 6

For the equation -(2t) = 12:
Divide both sides by -2 to solve for t:
-(2t)/-2 = 12/-2
t = -6

Thus, the solution to the equation |2t| - 5 = 7 is t = 6 or t = -6.