Part 1 of 2 Solve and graph the equation. |2t| = 4 Select the correct choice and, if necessary, fill in the answer box in your choice below.
OA. t = (Simplify your answer. Use a comma to separate answers as needed.)
OB. There is no solution.
To solve the equation |2t| = 4, we can consider two cases:
Case 1: 2t is positive:
If 2t is positive, then |2t| = 2t. So we have 2t = 4.
Dividing both sides of the equation by 2 gives us:
t = 2.
Case 2: 2t is negative:
If 2t is negative, then |2t| = -2t. So we have -2t = 4.
Dividing both sides of the equation by -2 gives us:
t = -2.
Therefore, the solutions to the equation |2t| = 4 are t = 2 and t = -2.
Graphically, these solutions can be represented as two points on the number line:
---------------------(-2)----------------(2)-------------------
So the correct choice is:
OA. t = -2, 2
To solve the equation |2t| = 4, we can rewrite it as two separate equations:
1) 2t = 4
2) -(2t) = 4
For equation 1, we solve for t:
2t = 4
Divide both sides by 2:
t = 2
For equation 2, we solve for t:
-(2t) = 4
Divide both sides by -2 (this will change the sign):
t = -2
So, the solution to the equation |2t| = 4 is t = 2 or t = -2.
Now, let's graph the equation to visualize the solutions.
To solve and graph the equation |2t| = 4, we need to find the values of t that satisfy the equation.
Part 1: Solving the equation
We start by removing the absolute value, which means we consider two cases: one when 2t is positive, and one when 2t is negative.
Case 1: 2t is positive
In this case, 2t = 4. Solving for t, we divide both sides of the equation by 2:
2t/2 = 4/2
t = 2
Case 2: 2t is negative
In this case, -2t = 4. Solving for t, we divide both sides of the equation by -2, which requires us to change the direction of the inequality:
-2t/(-2) = 4/(-2)
t = -2
So, the possible solutions for the equation |2t| = 4 are t = 2 and t = -2.
Part 2: Graphing the equation
To graph the equation |2t| = 4, we plot the solutions t = 2 and t = -2 on a number line:
-----o------o--------------
-2 0 2
The graph shows that the equation is satisfied at t = 2 and t = -2.
Therefore, the correct choice is:
OA. t = 2, -2