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How do you solve the equation #abs(3x-3)=8#?

Answer 1

#x_1=11/3#
#x_2=-5/3#

#abs(3x-3)=8#

What is Absolute value/ modulus? #(3x-3)# might be positive or negative but we only need the positive value of it which is 8.

To solve the equation, and find #x# we need to cancel off the modulus by adding #+-# sign to 8

#(3x-3)=+-8# #3x=+-8+3# #x=(+-8+3)/3#

#x_1=(8+3)/3=11/3# #x_2=(-8+3)/3=-5/3#

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Answer 2

Nathan Axel

To solve the equation (|3x - 3| = 8), you first isolate the absolute value term by setting it equal to both positive and negative values of 8:

[ 3x - 3 = 8 ] or [ 3x - 3 = -8 ]

Then, solve each equation separately:

For (3x - 3 = 8): [ 3x = 11 ] [ x = \frac{11}{3} ]

For (3x - 3 = -8): [ 3x = -5 ] [ x = -\frac{5}{3} ]

So, the solutions are (x = \frac{11}{3}) and (x = -\frac{5}{3}).

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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.