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How do you solve compound inequalities #8d<-64# and #5d > 25#?

Answer 1

Ethan Adkins

Let's look at each inequality individually first.

#8d<-64#

Dividing both sides by 8, we get:

#(cancel(8)d)/cancel(8) < -64/8#

#color(blue)(d < - 8#

#5d>25#

Dividing both sides by 5, we get:

#(cancel(5)d)/cancel(5) > 25/5#

#color(blue)(d>5#

#d# can take any value which is less than #-8# or greater than #5#

The values #d# will take on the number line are marked in blue. (The values #-8 and 5# are not included)

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Answer 2

Abigail Allen

To solve the compound inequalities \(8d < -64\) and \(5d > 25\), solve each inequality separately. For the first inequality \(8d < -64\), divide both sides by 8 to isolate \(d\), giving \(d < -8\). For the second inequality \(5d > 25\), divide both sides by 5 to isolate \(d\), resulting in \(d > 5\). Combining the solutions, we get \(d < -8\) or \(d > 5\).

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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.

How do you solve compound inequalities #8d&lt;-64# and #5d &gt; 25#?

How do you solve compound inequalities #8d<-64# and #5d > 25#?