How do you solve the inequality #2(x - 4)< 8(x + 1/2)#?

Answer 1

#x > -4/3#

Given #color(white)("XXX")2(x-4) < 8(x+1/2)#
Simplify both sides #color(white)("XXX")2x-4 < 8x + 4#
Add 4 to both sides #color(white)("XXX")2x < 8x +8#
Subtract #8x# from both sides #color(white)("XXX")-6x < 8#
Divide both sides by #(-6)# Remember that multiplying or dividing by a number less than zero requires that you reverse the inequality sign #color(white)("XXX")x > -4/3#
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Answer 2

To solve the inequality (2(x - 4) < 8(x + \frac{1}{2})), follow these steps:

  1. Distribute the constants and variables: (2x - 8 < 8x + 4)

  2. Move all terms involving the variable (x) to one side and constants to the other side: (2x - 8x < 4 + 8)

  3. Combine like terms: (-6x < 12)

  4. Divide both sides of the inequality by (-6). Remember to reverse the inequality sign when dividing by a negative number: (x > -2)

So, the solution to the inequality is (x > -2).

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Answer 3

To solve the inequality (2(x - 4) < 8(x + \frac{1}{2})), follow these steps:

  1. Distribute the factors: (2x - 8 < 8x + 4)

  2. Rearrange the terms to isolate the variable: (2x - 8x < 4 + 8)

  3. Combine like terms: (-6x < 12)

  4. Divide both sides by (-6). Note: Remember to reverse the inequality sign when dividing by a negative number. (x > -2)

So, the solution to the inequality is (x > -2).

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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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