What is the interval notation for: |2x-3|<7

Question

|2x-3|<7

and

x^2-x <= 12

Answer 1

l 2x - 3 l < 7 means that 2x - 3 is less than 7 units from zero on the number line.

So, -7 < 2x - 3 < 7

-4 < 2x < 10

-2 < x < 5 Solution set: (-2, 5)

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x² - x - 12 ≤ 0

(x - 4)(x + 3) ≤ 0

(x - 4)(x + 3) = 0 when x = 4 or -3

When x < -3, both factors are negative, so (x - 4)(x + 3) > 0

When -3 < x < 4, the two factors have opposite signs, so (x - 4)(x + 3) < 0

When x > 4, both factors are positive, so (x - 4)(x + 3) > 0

Solution set [-3, 4]