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How do you solve the equation #abs(2x-3)=3#?

Answer 1

See the entire solution process below:

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1)

#2x - 3 = -3#

#2x - 3 + color(red)(3) = -3 + color(red)(3)#

#2x - 0 = 0#

#2x = 0#

#(2x)/color(red)(2) = 0/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 0#

#x = 0#

Solution 2)

#2x - 3 = 3#

#2x - 3 + color(red)(3) = 3 + color(red)(3)#

#2x - 0 = 6#

#2x = 6#

#(2x)/color(red)(2) = 6/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 3#

#x = 3#

The solution is: #x = 0# and #x = 3#

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Answer 2

Savannah Anderson

To solve the equation |2x - 3| = 3, you set up two separate equations: 2x - 3 = 3 and 2x - 3 = -3. Then solve each equation individually for x.

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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.