How do you solve #-7+8abs(-7x-3)=73#?

Answer 1

See the entire solution process below:

First, add #color(red)(7)# to each side of the equation to isolate the absolute value term while keeping the equation balanced:
#color(red)(7) -7 + 8abs(-7x - 3) = color(red)(7) + 73#
#0 + 8abs(-7x - 3) = 80#
#8abs(-7x - 3) = 80#
Next, divide each side of the equation by #color(red)(8)# to isolate the absolute value function while keeping the equation balanced:
#(8abs(-7x - 3))/color(red)(8) = 80/color(red)(8)#
#(color(red)(cancel(color(black)(8)))abs(-7x - 3))/cancel(color(red)(8)) = 10#
#abs(-7x - 3) = 10#

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)

#-7x - 3 = -10#
#-7x - 3 + color(red)(3) = -10 + color(red)(3)#
#-7x - 0 = -7#
#-7x = -7#
#(-7x)/color(red)(-7) = (-7)/color(red)(-7)#
#x = 1#

Solution 2)

#-7x - 3 = 10#
#-7x - 3 + color(red)(3) = 10 + color(red)(3)#
#-7x - 0 = 13#
#-7x = 13#
#(-7x)/color(red)(-7) = 13/color(red)(-7)#
#x = -13/7#
The solution is: #x = 1# and #x = -13/7#
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Answer 2

To solve the equation -7 + 8| -7x - 3| = 73:

  1. Add 7 to both sides: 8| -7x - 3| = 80.
  2. Divide both sides by 8: | -7x - 3| = 10.
  3. Break into two cases: a) -7x - 3 = 10 b) -7x - 3 = -10
  4. Solve each case separately: a) -7x = 13 Divide by -7: x = -13/7 b) -7x = 7 Divide by -7: x = -1

Therefore, the solutions are x = -13/7 and x = -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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