How do you solve #5+8abs(-10n-2)=101#?

Answer 1

See a solution process below:

First, subtract #color(red)(5)# from each side of the equation to isolate the absolute value term while keeping the equation balanced:
#5 - color(red)(5) + 8abs(-10n - 2) = 101 - color(red)(5)#
#0 + 8abs(-10n - 2) = 96#
#8abs(-10n - 2) = 96#
Next divide each side of the equation by #color(red)(8)# to isolate the absolute value function while keeping the equation balanced:
#(8abs(-10n - 2))/color(red)(8) = 96/color(red)(8)#
#(color(red)(cancel(color(black)(8)))abs(-10n - 2))/cancel(color(red)(8)) = 12#
#abs(-10n - 2) = 12#

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

Solution 1:

#-10n - 2 = -12#
#-10n - 2 + color(red)(2) = -12 + color(red)(2)#
#-10n - 0 = -10#
#-10n = -10#
#(-10n)/color(red)(-10) = (-10)/color(red)(-10)#
#(color(red)(cancel(color(black)(-10)))n)/cancel(color(red)(-10)) = 1#
#n = 1#

Solution 2:

#-10n - 2 = 12#
#-10n - 2 + color(red)(2) = 12 + color(red)(2)#
#-10n - 0 = 14#
#-10n = 14#
#(-10n)/color(red)(-10) = 14/color(red)(-10)#
#(color(red)(cancel(color(black)(-10)))n)/cancel(color(red)(-10)) = -14/10#
#n = -14/10#
The Solutions Are: #n = 1# and #n = -14/10#
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Answer 2

To solve the equation 5 + 8|−10n − 2| = 101, follow these steps:

  1. Subtract 5 from both sides to isolate the absolute value term: 8|−10n − 2| = 96.
  2. Divide both sides by 8: |−10n − 2| = 12.
  3. Rewrite the equation as two separate equations, one with a positive and one with a negative absolute value: -10n - 2 = 12 and -10n - 2 = -12.
  4. Solve each equation separately for n: -10n = 14 (for the positive case) and -10n = -10 (for the negative case).
  5. Divide both sides by -10: n = -1.4 (for the positive case) and n = 1 (for the negative case).

So, the solutions are n = -1.4 and n = 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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