Question

Which of the following is in the solution set of the inequality –3 > –3t + 6?

Answer 1

The inequality –3 > –3t + 6 is solved by isolating the term containing t and dividing by –3, giving the solution t < 3. The solutions t = 3.96 and t = -1.03 do not align with the steps of this inequality.

Step-by-step explanation:

To solve the inequality –3 > –3t + 6, we first isolate the term containing the variable t on one side of the inequality. We can do this by subtracting 6 from both sides of the inequality, which gives us –9 > –3t. Then, to solve for t, we divide both sides of the inequality by –3. When dividing by a negative number, we must remember to reverse the inequality sign. Therefore, t < 3 is the solution. However, this process doesn't yield a specific numerical value. Hence, we cannot verify the solutions t = 3.96 or t = -1.03, as they seem unrelated to the original inequality provided.

Thus, the solution set for the inequality –3 > –3t + 6 is all t values less than 3, which is a different finding from previously stated solutions t = 3.96 and t = -1.03.

Answer 2

For this we want to switch the sides to start out.
-3t + 6 < -3
Now we want to subtract 6 from both sides...
-3t + 6 - 6 < -3 - 6
Simplify it.
-3t < -9
Now we want to reverse the inequality and multiply both sides by -1
(-3t) (-1) > (-9)(-1)
Simplify yet again.
3t > 9
Divide both sides by 3 now.
3t/3 > 9/3
Now we can say that t > 3.
Hope this helps!