How do you solve #|(x/2) + 3| = 3x -3#?

Answer 1
#|(x/2)+3|=3x-3# #x/2 + 3=+-(3x-3)# Therefore, #x/2 + 3=(3x-3) or (3-3x)# When, #x/2 + 3= 3x-3# #6=(5x)/2# #12=5x# #x=12/5# ^1st answer
When, #x/2 +3=3-3x# #(7x)/2=0# #7x=0# #x=0#
Therefore, #x=0 or x= 12/5#
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Answer 2

To solve the equation |(x/2) + 3| = 3x - 3, follow these steps:

  1. Split the equation into two cases: Case 1: (x/2) + 3 = 3x - 3 Case 2: (x/2) + 3 = -(3x - 3)

  2. Solve each case separately for x.

    Case 1: (x/2) + 3 = 3x - 3 Solve for x: x/2 + 3 = 3x - 3 x/2 - 3x = -3 - 3 x/2 - 3x = -6 x - 6x = -12 -5x = -12 x = (-12)/(-5) x = 12/5

    Case 2: (x/2) + 3 = -(3x - 3) Solve for x: (x/2) + 3 = -3x + 3 x/2 + 3x = 3 - 3 x/2 + 3x = 0 Multiply both sides by 2 to eliminate the fraction: x + 6x = 0 7x = 0 x = 0

  3. Check the solutions: Substitute each solution back into the original equation to ensure they are valid.

    For x = 12/5: |(12/5)/2 + 3| = 3(12/5) - 3 |6/5 + 3| = 36/5 - 3 |33/5| = 36/5 - 3 33/5 = 36/5 - 15/5 33/5 = 21/5 33 ≠ 21, so this solution is not valid.

    For x = 0: |0/2 + 3| = 3(0) - 3 |3| = 0 - 3 3 = -3 This is not true, so the solution x = 0 is also not valid.

  4. Therefore, the equation has no real solutions.

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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.

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.

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.

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.

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