Question

For which compound inequalities is 6 a solution? Select the statements that are true.

-5 < x < 6
-2 < x < 6
x < 2 or x 26
0x< 2 or x>6
O x < -5 or x > 0

Answer 1

The compound inequalities for which 6 is a solution are 'x < 2 or x ≥ 6' and 'x < -5 or x > 0'. In these cases, the 'or' condition satisfies the inclusion of the number 6.

Step-by-step explanation:

To determine for which compound inequalities the number 6 is a solution, we need to substitute the value of 6 into each inequality and verify whether the inequality holds true.

• For the inequality -5 < x < 6, when x is 6, the second part of the inequality (x < 6) is not satisfied, since 6 is not less than 6.
• The inequality -2 < x < 6 also does not hold true for x equals 6 for the same reason mentioned above.
• In the expression x < 2 or x ≥ 6, the first part (x < 2) is not true for x equals 6, but the second part (x ≥ 6) is true because 6 is equal to 6, thus satisfying the or condition.
• Finally, for the inequality x < -5 or x > 0, while x is not less than -5, it is greater than 0, satisfying the second part of the inequality.

Therefore, out of the provided options, the compound inequalities for which 6 is a solution are: x < 2 or x ≥ 6 and x < -5 or x > 0.