Solve for #x#? #3(x-4)<12 or 4(x+3)<12#

Answer 1

#x<8#

We have two inequalities that are linked with an "or", which means that so long as we have a valid #x# for one of the equations, it'll be part of the solution set (whereas if we had "and", we'd need the #x# values to be valid in both equations).

Let's solve them individually and see what we get:

Equation 1

#3(x-4)<12#
#x-4<4#
#x<8#

Equation 2

#4(x+3)<12#
#x+3<3#
#x<0#

Putting it together

We have #x<8# or #x<0#. Again, so long as we have a valid #x# value in one inequality, it's part of the solution.
#" OR "# means either of the conditions must be true.
#x<8#, since it includes all the solutions in #x<0# and more, is the final answer.
However, if it had been #x<0 " AND " x <8#, then BOTH conditions have to be true and the solution would be #x<0#
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Answer 2

To solve for (x), you need to solve each inequality separately.

  1. (3(x - 4) < 12): [3(x - 4) < 12] [3x - 12 < 12] [3x < 12 + 12] [3x < 24] [x < \frac{24}{3}] [x < 8]

  2. (4(x + 3) < 12): [4(x + 3) < 12] [4x + 12 < 12] [4x < 12 - 12] [4x < 0] [x < 0]

So, the solutions for (x) are: [x < 8] for the first inequality, and [x < 0] for the second inequality.

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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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