Question

Solve the inequality. which intervals are included in the solution? check all that apply. (negative infinity, 0) (0, 4] [4, 10) (10, 30] [30, infinity)

Answer 1

Without the specific inequality, it is not possible to determine which intervals are included in the solution. However, one would generally test values from each given interval in the inequality to see if they satisfy it, thus determining if an interval is part of the solution set.

Step-by-step explanation:

The intervals included in the inequality are (-∞ , -4) and (4, ∞)

Using the inequality expression given ;

x² - 16 > 0

We can factorize the expression x² - 16 thus

x² - 16

x(x - 4)+4(x - 4)

(x - 4)(x + 4) > 0

x + 4 > 0 or x - 4> 0

Now we have ;

x > -4 or x > 4

Therefore, the intervals for which are included in the solution are ;

(-∞, -4 ) and (4, ∞)

Complete Question:

Solve the inequality. x² -16 >0 which intervals are included in the solution? check all that apply. (negative infinity, 0) (0, 4] [4, 10) (10, 30] [30, infinity)

Answer 2

The intervals included in the inequality are (-∞ , -4) and (4, ∞)

Using the inequality expression given ;

• x² - 16 > 0

We can factorize the expression x² - 16 thus

x² - 16

x(x - 4)+4(x - 4)

(x - 4)(x + 4) > 0

x + 4 > 0 or x - 4> 0

Now we have ;

x > -4 or x > 4

Therefore, the intervals for which are included in the solution are ;

• (-∞, -4 ) and (4, ∞)

Complete Question:

Solve the inequality. x² -16 >0 which intervals are included in the solution? check all that apply. (negative infinity, 0) (0, 4] [4, 10) (10, 30] [30, infinity)