radical 2x-6 < 4 How to solve for x?

Question

Please also show how to plug in the zero and why do we plug in the zero

Answer 1

radical 2x-6 < 4

 

Assuming this means √(2x-6) < 4

 

Since you can't have a negative under a square root sign if working with real numbers, 2x-6 ≥ 0, x ≥ 3.

 

Now square both sides:

 

2x-6 < 16

 

2x < 22

 

x < 11

 

Putting the constraint we found earlier into it:

 

3 ≤ x < 11

Answer 2

The problem states radical 2x-6<4.

               ____

If this is √2x-6 <4 we square both sides to get 2x-6<16.

2x-6<16

2x<22

x<11         __                           __

If this is √2x -6<4 we have √2x <10 and squaring both sides we get 2x<100, x<50.

 CORRECTION:2x-6>0,2x>6,x>3

3<x<11

also, 2x>0, x>0

0<x<50

Corrections made courteous of Steve S. I looked at this problem several times and said something is missing but couldn't pinpoint it at the time.

Answer 3

Hi Madison;

2x-6 < 4

I do not know if you know the difference between < and >.  In the sixth grade, the way we remembered this is, The alligator is going to eat the bigger one.

2x-6 < 4

Let's isolate x.

Let's begin by adding 6 to both sides...

2x-6+6<4+6

2x<10

Let's divide both sides by 2...

(2x)/2<10

x<5

If 2 is negative, then < must be converted to >, as the alligator turns away from negativity.

 

Answer 4

Initial problem                                                               2x-6<4

Add 6 to both sides to isolate the "x" on one side              2x-6+6<4+6

                                                                                    2x<10

Divide each side by 2 to leave the x coefficient at 1            2/2x<10/2

                                                                                    1x<5

                                                                                     Answer x<5

 

I don't know what you mean by plugging in 0. You have to explain that.