How do you solve #14- 4k < 38#?

Answer 1

#k> -6#

We can treat this inequality like it's an equation. If our problem was instead #14-4k=38#, we would subtract #14# from both sides. We would do the same here to get:
#-4k<24#
Now, we divide both sides by #-4#, and here's the catch: Since we're dividing the inequality by a negative number, the direction of the sign will flip. This would even hold true of we're multiplying. We get:
#k> -6#
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Answer 2

#k> -6#

#14-4k<38#
Start by subtracting #14# on both sides
#14 - 4k - 14 < 38 - 14#
#-4k < 24#
Divide both sides by #-4# #(cancel(-4)k)/cancel(-4) < 24/(-4)#
#k > -6#

Note:

When you are solving an inequality, if you divide both sides by a negative sign, you MUST change the sign as well. If it was #<#, it will be #>#. Got it?
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Answer 3

See a solution process below:

First, subtract #color(red)(14)# from each side of the inequality to isolate the #k# term while keeping the equation balanced:
#14 - color(red)(14) - 4k < 38 - color(red)(14)#
#0 - 4k < 24#
#-4k < 24#
Now, divide each side of the inequality by #color(blue)(-4)# to solve for #k# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#(-4k)/color(blue)(-4) color(red)(>) 24/color(blue)(-4)#
#(color(red)(cancel(color(black)(-4)))k)/cancel(color(blue)(-4)) color(red)(>) -6#
#k color(red)(>) -6#
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Answer 4

To solve (14 - 4k < 38), follow these steps:

  1. Subtract 14 from both sides: (-4k < 24)
  2. Divide both sides by (-4) (note that dividing by a negative number reverses the inequality sign): (k > -6)

So, the solution to the inequality is (k > -6).

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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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