The equation |x - 4|_>, when solved is ?

Answer 1

If you are saying the following : (if not, then the following solution is wrong!)

| x - 4 | > y

Then you get rid of the absolute brackets and make 2 separate equations, switching the inequality and negating the right side of the equation for the 2nd :

Equation 1 : x - 4 > y

Equation 2 : x - 4 < -y

Solve Equation 1 : (add 4 to both sides)

x - 4 > y

x > y + 4

Solve Equation 2 : (add 4 to both sides)

x - 4 < -y

x < -y + 4

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Always check your work!

Set y = 40 (I selected a random number)

( x - 4 ) must be (>= 41) or (<= -41)

Solved Equation 1 ; x > 40 + 4... x > 44

This makes sense, because x would need to be 45 or greater in order for x - 4 >= 41

CORRECT!

Solved Equation 2 : x < -40 + 4.... x < -36

This makes sense, because x would need to be -37 or less in order for x - 4 <= -41

CORRECT!