Solve the following compound inequality.

Question

-4x<_16 and 4x+5<25

Answer 1

To solve the first inequality, we divide both sides by -4, remembering to flip the inequality sign because we are dividing by a negative number:

-4x ≤ 16

x ≥ -4

To solve the second inequality, we subtract 5 from both sides:

4x + 5 < 25

4x < 20

x < 5

Now, we need to determine the overlapping solution for both inequalities.

From the first inequality, we know that x must be greater than or equal to -4.

From the second inequality, we know that x must be less than 5.

Considering both conditions, we can say that x lies between -4 and 5 (excluding -4 and 5).

In interval notation, this can be written as: (-4, 5)