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How do you graph and solve #|x-5|+|2-2x|=7 #?

Answer 1

Avery Alexander

#x = {0,4}#

#abs(x-5)=7-2abs(x-1)# gives

1) #x-5=7-2abs(x-1)# #->x-12=2abs(x-1)#

1-a) #x-12=2(x-1)# #->-12=x-2# #->x=10#

1-b) #x-12=-2(x-1)# #->3x=12+2# #->x=14/3#

2) #-(x-5)=7-2abs(x-1)# #->-x-2=-2abs(x-1)# #->x+2=2abs(x-1)#

2-a) #x+2=2(x-1)# #->2=x-2# #->x=4#

2-b) #x+2=-2(x-1)# #->3x+2=2# #->x=0#

Checking the solutions

#x = {-14/3,0,4,10}#

we keep the very solutions: #x = {0,4}#

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Answer 2

Eva Abramson

To graph and solve the equation ( |x-5| + |2-2x| = 7 ), you would first isolate the absolute value expressions and create separate cases for each. Then, you would solve for the possible values of x in each case and plot those points on a graph. Finally, you would connect the points to form the graph of the equation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.