.Solve and graph the equation.
|8t|=72
Select the correct choice and, if necessary, fill in the answer box in your choice below.
To solve the equation |8t| = 72, we can split it into two separate equations:
1) 8t = 72
2) 8t = -72
For equation 1, we can solve for t by dividing both sides by 8:
t = 9
For equation 2, we can also solve for t by dividing both sides by 8:
t = -9
So the two solutions to the equation are t = 9 and t = -9.
To graph the equation, we can plot these two solutions on a number line:
<--------------------------x---------0----->
-9 9
So the graph would have two points labeled -9 and 9 on the number line.
Solve the equation. Graph and check your solutions.
x+1=12
Solve the equation for x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
To solve the equation x + 1 = 12, we can isolate x by subtracting 1 from both sides of the equation:
x + 1 - 1 = 12 - 1
This simplifies to:
x = 11
To graph the equation, we can plot the solution x = 11 on a number line:
<------------------x--------------->
11
So the graph would have a point labeled 11 on the number line.
To check the solution, we substitute x = 11 back into the original equation:
11 + 1 = 12
This is true, so the solution x = 11 is correct.
To solve the equation |8t|=72, we need to consider two cases: when 8t is positive and when it is negative.
Case 1: 8t > 0
In this case, the absolute value of 8t is simply 8t. So we have 8t = 72. To solve for t, divide both sides of the equation by 8: t = 72/8 = 9.
Case 2: 8t < 0
In this case, the absolute value of 8t is the negative of 8t, which means we have -8t = 72. To solve for t, divide both sides of the equation by -8 (remember that when you divide or multiply both sides of an equation by a negative number, you need to reverse the direction of the inequality): t = 72/(-8) = -9.
Therefore, the two solutions to the equation |8t|=72 are t = 9 and t = -9.
To graph the equation, you can plot the two solutions on a number line. Place a point at 9 and another point at -9. These two points indicate where the absolute value of 8t is equal to 72.