Question

Graph the inequality |x| + |y| < 1
Please give the step by step solution for the above problem.

Thanks in Advance

Answer 1

for x and y >=0 (i.e. in quadrant 1)
you can plot x+y=1
or in slope-intercept form: y= -x + 1
plot that line and make it dotted. be sure both x and y are positive (in other words don't plot the line so either x or y is negative) that is part of the answer

Answer 2

then look at the case where x is positive and y is negative (quadrant 4)
x -y = 1
y= x -1
plot that line in quadrant 4, and make it dotted.

Answer 3

do the same for the other two quadrants.
you will get a diamond shape, with dotted lines as the sides
fill in the diamond to show all the values inside the diamond will make the original inequality true.

Answer 4

Thanks for the answer