|2x−10|> 0 what is the value of x

x< 5 or x>5      

Step-by-step explanation:

With absolute value inequalities we have two solutions, one positive and one negative.  Remember when we take the negative, we flip the inequality

2x-10 > 0   or              2x-10 < -0

Add 10 to each side

2x-10+10 > 0+10           2x-10 + 10 < 0 + 10

2x > 10                        2x < 10

Divide by 2

2x/2 >10/2                  2x/2 < 10/2

x >5                                  x < 5

x< 5 or x>5          

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: