Directions: Select all correct answers. Solve the quadratic inequality. -2(x + 3)(x - 7) ≤ 0 Select all...

Question

Directions: Select all correct answers.
Solve the quadratic inequality.
-2(x + 3)(x - 7) ≤ 0
Select all intervals that are in the solution set of the inequality.
☐ (-∞, -3]
☐ (-∞, 7]
☐ (-3, 7)
☐ [-3, 7]
☐ [-3, ∞)
☐ [7, ∞)

SnapAndSolve AI · Accepted Answer

To solve the inequality -2(x + 3)(x - 7) ≤ 0, we first find the roots of the equation -2(x + 3)(x - 7) = 0, which are x = -3 and x = 7.

The inequality changes sign at these points. We test intervals around the roots to determine where the inequality holds:

For x in (-∞, -3], the expression is positive.
For x in (-3, 7), the expression is negative.
For x in [7, ∞), the expression is positive.

Thus, the solution set is [-3, 7].

Correct intervals:

☐ (-∞, -3]
☐ (-∞, 7]
☐ (-3, 7)
☑ [-3, 7]
☐ [-3, ∞)
☐ [7, ∞)

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Directions: Select all correct answers. Solve the quadratic inequality. -2(x + 3)(x - 7) ≤ 0 Select all...

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