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How do you solve and write the following in interval notation: #5(5-2x)≥40-7x#?

Answer 1

Nathan Axel

#x in (oo, -5]#

#5(5-2x)≥40-7x#

expand bracket

#25-10x≥40-7x#

subtract 25

#-10x≥15-7x#

add 7x

#-3x≥15#

divide by 3

#-x≥5#

times -1 (and switch inequality sign)

# x le -5#

interval notation:

#implies x in (oo, -5]#

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Answer 2

Hazel Anglin

To solve the inequality 5(5 - 2x) ≥ 40 - 7x:

Distribute the 5 on the left side: 25 - 10x ≥ 40 - 7x
Move all terms containing x to one side by adding 7x and subtracting 25 from both sides: -10x + 7x ≥ 40 - 25 -3x ≥ 15
Divide both sides by -3, remembering to reverse the inequality sign when dividing by a negative number: x ≤ -5

The solution in interval notation is (-∞, -5].

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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.