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How do you solve and write the following in interval notation: #8- 5x<=23#?

Answer 1

Kennedy Adams

#[-3,+oo)#

#"Isolate " -5x" by subtracting 8 from both sides"#

#cancel(8)cancel(-8)-5x<=23-8#

#rArr-5x<=15#

#"divide both sides by - 5"#

#color(blue)"Note ""when multiplying/dividing an inequality"# #"by a negative quantity, the inequality sign is "color(red)"reversed"#

#(cancel(-5) x)/cancel(-5)>=15/(-5)larrcolor(red)" reverse sign"#

#rArrx>=-3" is the solution"#

#[-3,+oo)larr" in interval notation"#

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Answer 2

Hazel Anglin

To solve the inequality 8 - 5x ≤ 23, follow these steps:

Subtract 8 from both sides of the inequality: 8 - 5x - 8 ≤ 23 - 8 -5x ≤ 15
Divide both sides by -5. Note that when dividing by a negative number, the direction of the inequality sign changes: -5x / -5 ≥ 15 / -5 x ≥ -3

So, the solution to the inequality is x ≥ -3.

Now, to express the solution in interval notation, we write it as [-3, ∞). This represents all real numbers greater than or equal to -3.

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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.

How do you solve and write the following in interval notation: #8- 5x&lt;=23#?

How do you solve and write the following in interval notation: #8- 5x<=23#?