How do you solve # 5 |x - 3| >=20#?

Answer 1

#x>=7 or x<= -1#. In interval notation, solution is #(-oo , -1] uu [7, +oo)#

#5|x-3|>=20 or |x-3|>=4 :. x-3>=4 or x>=7# OR #5|x-3|>=20 or |x-3|>=4 :. x-3<= -4 or x<= -1# In interval notation solution is #(-oo , -1] uu [7, +oo)#[Ans]
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Answer 2

To solve ( 5 |x - 3| \geq 20 ):

  1. Divide both sides by 5: ( |x - 3| \geq 4 ).

  2. Solve for two cases:

    • ( x - 3 \geq 4 ) and ( x - 3 \leq -4 ).
  3. Solve each case separately:

    • Case 1: ( x - 3 \geq 4 )
      • Add 3 to both sides: ( x \geq 7 ).
    • Case 2: ( x - 3 \leq -4 )
      • Add 3 to both sides: ( x \leq -1 ).
  4. Combine the solutions:

    • The solution is ( x \geq 7 ) or ( x \leq -1 ).

Therefore, the solution to ( 5 |x - 3| \geq 20 ) is ( x \geq 7 ) or ( x \leq -1 ).

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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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