Find the solution to the inequality: x^2 + 4x < 5.

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Question: Find the solution to the inequality: x^2 + 4x < 5.

Options:

Correct Answer: (-5, 1)

Solution:

Step 1: Rearrange: x^2 + 4x - 5 < 0. Step 2: Factor: (x + 5)(x - 1) < 0. Step 3: Test intervals: solution is (-5, 1).

Find the solution to the inequality: x^2 + 4x < 5.

Find the solution to the inequality: x^2 + 4x < 5.

Step 1: Rearrange the inequality by moving 5 to the left side: x^2 + 4x - 5 < 0.
Step 2: Factor the quadratic expression: (x + 5)(x - 1) < 0.
Step 3: Identify the critical points by setting each factor to zero: x + 5 = 0 gives x = -5, and x - 1 = 0 gives x = 1.
Step 4: Test intervals around the critical points (-∞, -5), (-5, 1), and (1, ∞) to see where the product (x + 5)(x - 1) is negative.
Step 5: The solution is the interval where the inequality holds true, which is (-5, 1).

Inequalities – Understanding how to manipulate and solve quadratic inequalities.
Factoring – Ability to factor quadratic expressions to find critical points.
Interval Testing – Using test points in intervals to determine where the inequality holds true.