Final answer:
The solution to the inequality 6x - 20 < 8x + 4 is any number greater than -12. Upon comparing the options, only -11 is greater than -12, making option (b) the correct answer.
Step-by-step explanation:
The student's question pertains to solving an inequality of the form 6x - 20 < 8x + 4. To find which option represents a solution to this inequality, we need to isolate x on one side. First, we'll subtract 8x from both sides to get: -2x - 20 < 4. Next, we add 20 to both sides of the inequality, resulting in -2x < 24. Finally, we divide both sides by -2, remembering to reverse the inequality sign because we are dividing by a negative number, to get x > -12. We can now evaluate each of the given options to see which one is greater than -12.
- (a) -13 is not greater than -12.
- (b) -11 is greater than -12.
- (c) -12 is not greater than -12, it is equal.
- (d) -14 is not greater than -12.
The correct answer is (b) -11 because it is the only number that is greater than -12.
Correct Question
If 6x-20 < 8x 4, which of the following represents a solution to the inequality?
(a) -13
(b)-11
(c)-12
(d)-14