How do you solve the inequality x^2<=abs(4x-3) and write your answer in interval notation?

1 Answer
Oct 1, 2017

x^2 <= abs(4x - 3)

so, we have either x^2 <= 4x - 3 or x^2 <= -(4x - 3)

i.e. x^2 - 4x + 3 <= 0 or x^2 + 4x - 3 <= 0

solving x^2 - 4x + 3 = 0, we x = 1 or x = 3

Hence, 1 <= x <= 3

Solving x^2 + 4x - 3 = 0 using the quadratic formula gives:

x = -2 +- sqrt7

Hence, -2 - sqrt7 <= x <= -2 + sqrt7

Using interval notation we have:

[-2 - sqrt7, -2 + sqrt7] OR [1, 3]

:)>