How do you graph and solve #|2x – 3| – 6 = –1#?

Question

Savannah Anderson · Accepted Answer

#-1=x=4# When you have an absolute value equation, you isolate the absolute value before trying anything else. # |2x-3|-6=-1# becomes #|2x-3|=5# We have to note that there are two solutions to absolute value equations, since #|-a|=a# and #|a|=a# In other words, #2x-3=5# and #2x-3=-5# both give you the final answer of #|2x-3|=5#. #2x-3=5# #2x=8# #x=4# #2x-3=-5# #2x=-2# #x=-1# When we plug in these values, we find out that they both work. Therefore, #-1=x=4#

Eva Abramson · Answer

undefined To graph and solve |2x - 3| - 6 = -1, you first isolate the absolute value expression. Add 6 to both sides to get |2x - 3| = 5. Then, split the equation into two cases: 2x - 3 = 5 and 2x - 3 = -5. Solve each case separately to find potential solutions for x. After finding the solutions, plot them on a number line and determine the intervals where the absolute value expression is equal to 5. Finally, test a value from each interval in the original equation to confirm the solutions.