How do you solve #3/4(x - 2) - 1/3(5 - 2x) < -2#?

Answer 1
#3/4(x - 2) - 1/3(5 - 2x) < -2#

Multiply both sides by 12 to get

#9(x-2)-4(5-2x) < -24#

Now

#9(x-2)-4(5-2x)#
#=9x-9*2-4*5-4(-2x)#
#= 9x-18-40+8x#
#=17x-58#

So

#17x-58 < -24#

Add 58 to both sides to get

#17x < 34#

Divide both sides by 17 to get

#x < 2#

With inequalities you can perform any of the following operations while preserving the truth of the inequality:

(1) Add or subtract the same value on both sides. (2) Multiply or divide both sides by the same positive value. (3) Multiply or divide both sides by the same negative value and reverse the inequality.

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Answer 2

To solve the inequality ( \frac{3}{4}(x - 2) - \frac{1}{3}(5 - 2x) < -2 ), follow these steps:

  1. Distribute the fractions and simplify both sides of the inequality.
  2. Combine like terms and isolate the variable (x).
  3. Solve for (x).
  4. Check the solution to ensure it is valid for the original inequality.

After solving, you should get the solution set for (x).

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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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