Answer:
Explanation:
If -2/3, -1.5, and -5 are solutions to an inequality in x, then we know that when we substitute these values for x in the inequality, the inequality is true. On the other hand, if 2, 0, or 100 are substituted for x, the inequality is false.
We can use this information to write the inequality as follows:
x < -1.5 OR x > -5
To see why this inequality works, let's substitute the given values and test it:
When x = -2/3: -2/3 < -1.5 is true.
When x = -1.5: -1.5 < -1.5 is false, but -1.5 > -5 is true, so the inequality is true.
When x = -5: -5 < -1.5 is false, but -5 > -5 is false, so the inequality is true.
When x = 2: 2 < -1.5 is false, and 2 > -5 is true, so the inequality is true.
When x = 0: 0 < -1.5 is false, and 0 > -5 is true, so the inequality is true.
When x = 100: 100 < -1.5 is false, and 100 > -5 is true, so the inequality is true.
Therefore, the inequality x < -1.5 OR x > -5 fits the given information.