What is the solution to /2x-14/_> -3 ?

Question

By the way those are absolute value lines around the 2x-14 and that is supposed to be a greater than or equal to symbol. Any help is greatly appreciated!

Answer 1

|2x-14| > -3

2x-14 > -3
2x > 11
x > 5.5


-(2x-14) >-3
-2x +14 > -3
-2x > -17
2x <= 17
x <= 8.5

x is greater than 5.5 and less than equal to 8.5. They overlap. Meaning every real number is a solution.

Answer 2

Does this say the absolute value of the quantity 2x-14 is greater than or equal to -3? If so, the answeris the set of real numbers because the absolute value of anything is always greater than any negative.

Answer 3

All real numbers. The absolute value of any number is positive, since it is the distance from 0. Therefore the absolute value of 2x-14 is greater than or equal to -3 when x is any real number

Answer 4

We have 2 answers for that since the equation calls for another set of equations namely 2x-14 _> -3 U -(2x-14) _> -3.

(U stands for Union.)

We should have a positive and a negative for the equation.

2x-14 _> -3
2x _> 11
2x/2 _> 11/2
x _> 11/2

Next step:

-(2x-14) _> -3
-2x+14 _> -3
-2x _> -17
-2x/-2 _< -17/-2 (Dividing a negative number to both sides of the equation changes the sign of less than to greater than or vice-versa. Applicable only when an inequality is shown.)

x _< 17/2

x _> 11/2 U x _< 17/2
=11/2 _< x _< 17/2
=5.5 _< x _< 8.5

Answer 5

|2x - 14| >= -3

This means that either +(2x - 14 ) >= -3
or that -(2x - 14) >= -3.

First equation :

2x - 14 >= -3
Add 14 to both sides.
2x >= 11
Divide both sides by 2.
x >= 11/2

Second equation :
-(2x - 14) >= -3
Multiply out the minus sign, which is actually -1.
-2x + 14 >= -3
Subtract 14 from both sides.
-2x >= -17
Divide both sides by -2.
When you do that, the >= sign changes to a <= sign.
x <= 17/2

The solutions are x >= 11/2 and x <= 17/2
which is written as 11/2 <= x <= 17/2.

Answer 6

you must remeber thre are always two answers to absolute value questions, one for x_>0 and one for x<0 where you add a
"-" sign in front for x<0.

As such for x_>0:

2x-14_>-3

2x_>11

x_>11/2

And for x<0:

-(2x-14)_>-3

-2x+14_>-3

-2x/-2_>-17/-2(rember when divided by negative the equality sign reverses)

x_<17/2

As such the solutions are x_>11/2 and x_<17/2 which in turn translates that x is true for every real number in the interval
(-infinity,infinity)

Answer 7

|2x-14|>0>-3
Therefore the inequality holds for any given x

Answer 8

/any real number/>_0; 0>-3
/any real number/>-3; /2x-14/>_ -3
/2x-14/=any real number
2x-14=any real number
2x=any real number
x=any real number