contestada

Consider the following sets.
U = {all real number points on a number line}
A = {solutions to the inequality 3x+4>13}
B = {solutions to the inequality 1/2x+3<4}
For which values of x is A U B =ø

Respuesta :

Answer:

[2,3] is the answer

assuming you didn't have equal symbols under the inequality signs, you know [tex]\le[/tex] and [tex]\ge[/tex].

Step-by-step explanation:

Ok let's solve 3x+4>13 or 1/2 x+3<4.

Let's begin with 3x+4>13.

3x+4>13

Subtract 4 on both sides:

3x>9

Divide both sides by 3:

x>3

Now the other 1/2 x +3<4.

Subtract 3 on both sides:

1/2 x<1

Multiply both sides by 2:

x<2

So we have x>3 or x<2

If we graph this, this will give us better idea of what is and isn't a solution.

~~~~~~~~O                            x<2

                             O~~~~~~ x>3

------------(2)---------(3)---------

The only numbers not included are between 2 and 3 (inclusive).

So if x is between [2,3] then A or B has no solution.

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