Solve each inequality. Graph each solution set.?

Question

1.) |x| >or = to 2

2.) |x+1| < or = to 3

3.) |3x| < 6

4.) |2x| > or = to -64



These are my answers (wondering if it's right)

1.) {x| -2 > or = to x > or = to 2}

2.) {x|x < or = to 2 (or) x > or = 4}

3.) |3x| < 6

4.) {x| -32 > or = to x > or = to 32}

Answer 1

go to this website, will solve any equation for you

http://www.quickmath.com/

Answer 2

1) |x| >= 2 --> X >= 2 or X <= -2

2) |x+1| <= 3 --> -4 <= X <= 2

3) |3x| < 6 --> -2 < X < 2

4) |2x| >= -64 --> X e R [assuming the set of Reals]

You didn't solve #3, and you might want to re-read your answer to #1:
{ x | -2 >= x >= 2}

Answer 3

1.)
|x| >= 2
x >= 2 or x <= -2

2.)
|x + 1| <= 3
x + 1 <= 3 or x + 1 >= -3
x <= 2 or x >= -4
-4 <= x <= 2

3.)
|3x| < 6
3x < 6 or 3x > -6
x < 2 or x > -2
-2 < x < 2

4.)
|2x| >= -64
Since you can't have a absolute value with a negative value, this problem is unsolvable.

to have it solve and graphed, go to www.quickmath.com and type the problems in like i have them.

Answer 4

In the 1'st case, the disjoint set x ≥ 2 and x ≤ -2 fit the requirements

In the 2'nd case, -4 ≤ x ≤ 2

In the 3'rd case -2 < x < 2

And the the 4'th problem x = any number since the absolute value of x ( |x| ) is alway ≥ 0 ≥ -64 (or negative *anything* )


Doug