2. Solve the nonlinear inequality. Express the solution...

2. Solve the nonlinear inequality. Express the solution using interval notation a) (x-2)(x+3) < 0 b) x^2 - 3x - 18 ? 0 c) 2x^2 + x ? 1 d) 3x^2 - 3x < 2x^2 + 4 e) (2x + 1) / (x - 5) ? 3 f) 1 + 2 / (x + 1) ? 2 / x g) (x + 2) / (x + 3) ? (x - 1) / (x - 2)

Transcript

00:02 Okay, nonlinear inequality, the solution using interval notation.

00:07 So for this first one, this one's actually the easiest one because it's already kind of solved for x.

00:15 So x is less than 2 or x is less than a negative 3.

00:22 So then you have negative 3 is less than x, which is less than 2.

00:28 So that's for a.

00:30 Then for this one, you have x is minus 6 times x plus 3 is less than or equal to 0.

00:39 So then you have x is greater than or equal to a positive 6 or x is less than or equal to a negative 3.

00:46 Then if i bring this one over to the other side, i have 2x plus squared plus x minus 1 is less than or equal to 0.

00:55 So then when i go and solve this, x is less than or equal to negative 1 or x is greater than or equal to 1 half.

01:05 And so that's the answer to c.

01:10 Just going to box off my answers.

01:12 Then for d, i'm going to bring this stuff over to the other side.

01:17 So i have x squared minus 3x minus 4 is less than 0.

01:24 So then i would go x minus 4 times x plus 1 is less than 0.

01:33 So then i have x is less than 4 or x is greater than a negative 1.

01:42 Then i'm going to multiply both sides by x minus 5.

01:49 So then i have 2x plus 1 is less than or equal to 3 times x minus 5.

01:57 So then i have 2x plus 1 is less than or equal to 3x minus 15.

02:04 So then i have negative x is less than or equal to negative 16.

02:09 So x is, i have to flip my inequality, is greater than or equal to the positive 16.

02:16 And then for f, i'll do f down here.

02:20 So i'm going to do 1 over 1 plus 2 over x plus 1 plus or actually minus 2 over x.

02:33 And so i'm going to set up common denominator of x times x plus 1.

02:44 And then x times x plus 1...

Question

2. Solve the nonlinear inequality. Express the solution using interval notation a) (x-2)(x+3) < 0 b) x^2 - 3x - 18 ? 0 c) 2x^2 + x ? 1 d) 3x^2 - 3x < 2x^2 + 4 e) (2x + 1) / (x - 5) ? 3 f) 1 + 2 / (x + 1) ? 2 / x g) (x + 2) / (x + 3) ? (x - 1) / (x - 2)

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