Question

Solve the inequality |x + 4| < |2x|

Answer 1

See image below for answer:)

Explanation:

FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer 2

Below in bold.

Explanation:

One way to do these is to square both sides:

(x + 4)^2 < 4x^2

x^2 + 8x + 16 < 4x^2

3x^2 - 8x - 16 > 0

Let this = 0:

3x^2 - 8x - 16 = 0

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

x = -4/3, 4.

So the critical points are -4/3 and 4.

Make a table:

x < - 4/3 -4/3 +< x <= 4 x > 4

3x + 4 <0 > 0 > 0

x - 4 <0 < 0 > 0

(3x+4)(x-4) >0 <0 > 0

So the solution is x < -4/3 or x > 4

or in interval notation:

(-∞, -4/3) U (4, ∞)