How do you graph and solve # |2x-5| = -1#?

Question

How do you graph and solve # |2x-5| >= -1#?

Nathan Axel · Accepted Answer

Just find when #2x-5# is negative and put a negative sign to "make" it positive for the absolute part. Answer is:

#|2x-5|> -1# for every #x inRR#

They are never equal.

Quick solution The left part of the equation is an absolute, so it is always positive with a minimum of 0. Therefore, the left part is always: #|2x-5|>=0> -1# #|2x-5|> -1# for every #x inRR# Graph solution #|2x-5|# This is negative when: #2x-5<0# #2x<5# #x<5/2# And positive when: #2x-5>0# #2x>5# #x>5/2# Therefore, for you must graph: #-(2x-5)=-2x+5# for #x<5/2# #2x-5# for #x>5/2# These are both lines. Graph is: graph{|2x-5| [-0.426, 5.049, -1.618, 1.12]} As we can clearly see, the graph never passes through #-1# so the equal part is never true. However, it is always greater than #-1# so the answer is: For every #x inRR# (which means #x in(-oo,+oo)#

Eva Adamson · Answer

undefined To graph and solve the inequality |2x - 5| ≥ -1, first, recognize that the absolute value of any expression is always non-negative. Therefore, |2x - 5| will always be greater than or equal to 0. Hence, the inequality |2x - 5| ≥ -1 is always true for all real values of x. Therefore, the solution to the inequality is all real numbers.

How do you graph and solve # |2x-5| &gt;= -1#?

How do you graph and solve # |2x-5| >= -1#?