Question

X(x-6) < 7

Solve the quadratic inequality. Write the solution set in interval notation.

Answer 1

• - 1 < x < 7 or x ∈ (- 1, 7)

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Given inequality

• x(x - 6) < 7

Distribute and simplify, then find the x-intercepts:

• x(x - 6) < 7
• x² - 6x < 7
• x² - 6x - 7 < 0
• x² - 7x + x - 7 < 0
• x(x - 7) + (x - 7) < 0
• (x + 1)(x - 7) < 0

The x- intercepts are:

• x + 1 = 0 and x - 7 = 0
• x = - 1 and x = 7

Since the leading coefficient is positive, the graph opens up, so the interval between the x-intercepts is negative:

• - 1 < x < 7 or x ∈ (- 1, 7)