solve the compound inequality 3x-2<=2-x or 5x-1>3x+5?

Question

what is the answere in interval notation?

Answer 1

3x - 2 <= 2 - x
4x <= 4
x <= 1

or

5x - 1 > 3x + 5
2x > 6
x > 3

(-infinity, 1] U (3, +infinity)

Assuming that the 2 problems go with each other.

Answer 2

For the first part,
3x - 2 ≤ 2 - x. [Add (x + 2) to both sides.]
4x ≤ 4. [Divide by 4.]
x ≤ 1.

For the second part,
5x - 1 > 3x + 5. [Add (-3x + 1) to both sides.]
2x > 6. [Divide by 2.]
x > 3.

For an "OR" statement to be true, either of the two conditions must be true. The solution set is the set of all x such that
x ≤ 1 or x > 3.

In interval notation, it would be: (-∞, 1] or (3, ∞).

Answer 3

The solution is very simple and equivalent:
3x+5<5x-1 or 2-x>=3x-2

Answer 4

4x<=4 x<=1
2x>6 x>3

Since you say or that means x can be either in interval 1 or 2.

so: x is in (-inf, 1] U (3, inf)

"AND" would have meant no solutions.

Answer 5

1. Get all of the numbers (no x's) all to one side of the equation.
2. Simplify (combine like terms).
3. Combine the two equations and you should end up with x=.....
(your answer)!!!

Answer 6

just rearrange the x

for left side eqn: x = 1
for righte isde eqn: x = 3

henc