Write a specific system of linear inequalities that is equivalent to |y|<x where x>0. Graph the System. Hint: To generate your system, think about CASE I and CASE II.

Question

Do they want us to make linear equations based on numbers that are not equal to 0? Honestly, I have no idea what to do.

Answer 1

Case 1 is when you consider what is inside the absolute value symbols as positive (so: y < x) and Case 2 is when you consider what is inside the absolute value signs as negative (so: -(y) < x or y > -x)

Answer 2

absolute value has the definition

|a|=a if a≥0

|a|=-a if a<0 ,,,if a =-11 then |-11|=-(-11)=11

so |y|<x has two possibilities

1; y≥0 ,,,,y<x

2; y<0 ,,,,-y<x which is same as y>-x

draw two lines, y=x and y=-x

for x>0 the area below y=x for y>0 and area above y=-x for y<0

are the solution (x,y) points where |y|<x

note since problem specifies x>0 not x≥0 and |y|<x not |y|≤x

the point (0,0) is not part of the solution set.

Answer 3

Absolute value equations can be written as two equations:

|thing| = other

thing = other

-thing = other

Inequalities are the same:

1. y <x

***

1. -y<x

Divide both sides by -1, flip the inequality when dividing both sides or multiplying both sides by -1

y > -x