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Which compound inequality has no solution?

A. xs-2 and 2x > 6
B. xs-1 and 5x < 5
C. xs-1 and 3x²-3
D. xs-2 and 4x < -8

1 Answer

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Final answer:

To determine which compound inequality has no solution, we evaluate each option by solving the inequalities separately and checking for common values of x. Option A and Option D have no common values of x, so the compound inequalities have no solution.

Step-by-step explanation:

To determine which compound inequality has no solution, we need to analyze each option and see if there are any values of x that make both inequalities true. Let's evaluate each option:



A. xs-2 and 2x > 6

B. xs-1 and 5x < 5

C. xs-1 and 3x²-3

D. xs-2 and 4x < -8



By solving each inequality, we can determine if there are any common values for x. If there are no common values, then the compound inequality has no solution.



A. For xs-2 and 2x > 6, solving both inequalities separately:

xs-2: x > 2

2x > 6: x > 3

There is no common value for x that satisfies both inequalities, so the compound inequality has no solution.



Using the same approach, we can evaluate options B, C, and D:



B. For xs-1 and 5x < 5, solving both inequalities separately:

xs-1: x > 1

5x < 5: x < 1

Again, there is no common value for x that satisfies both inequalities, so the compound inequality has no solution.



C. For xs-1 and 3x²-3, solving both inequalities separately:

xs-1: x > 1

3x²-3: x² > 1

The second inequality can be further simplified by subtracting 1 from both sides: x²-1 > 0. This represents a parabola with roots at x = -1 and x = 1. Since the inequality is x > 1, the only common value with xs-1 is x = 1. Thus, this compound inequality has a solution.



D. For xs-2 and 4x < -8, solving both inequalities separately:

xs-2: x > 2

4x < -8: x < -2

Again, there is no common value for x that satisfies both inequalities, so the compound inequality has no solution.

User Jenya
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