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How do you solve the inequality #-5/6d+8>13#?

Answer 1

#d<-6#

We start off with #(-5)/6d+8>13#. My goal is to isolate #d# on one side of the expression. My first step would be to subtract #8# on both sides, making the expression now #(-5)/6d>5#.

Now, I want to get #d# alone, so I would divide by #(-5)/6# on both sides, making the expression now show #d<(5)/(-5/6)#, which can be rewritten as #d<5*(-6/5)#. The #-5*(-6/5)#will divide out (like so:#cancel(5)*(-6/cancel(5))#), leaving #d<-6#.

Please note that the sign changed when I divided #(-5)/6# on both sides. This is because when I multiply or divide by a negative number, the sign of the expression changes, from #<# to #># or vice versa.

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Answer 2

Savannah Anderson

To solve the inequality (-\frac{5}{6}d + 8 > 13), first subtract 8 from both sides to isolate the term involving (d).

(-\frac{5}{6}d > 5)

Next, multiply both sides by (-\frac{6}{5}) to solve for (d). Remember, when multiplying or dividing by a negative number, flip the inequality sign.

(d < -\frac{6}{5} \times 5)

(d < -6)

So, the solution to the inequality is (d < -6).

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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 the inequality #-5/6d+8&gt;13#?

How do you solve the inequality #-5/6d+8>13#?