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rusak2 [61]
3 years ago
14

What is the solution to the inequality

Mathematics
2 answers:
Alika [10]3 years ago
5 0

<u>Answer:</u>

p > 5, p < -8

<u>Step-by-step explanation:</u>

We are given the following inequality and we are to find its solution:

-6+|2p+3|>7

Adding 6 to both sides to get:

-6+6+|2p+3|>7+6

|2p+3|>13

We know the absolute rule that \mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:\:a.

So 2p+3>13 or 2p+3

2 p > 1 3 - 3, 2 p < - 1 3 - 3

2 p > 1 0, 2 p < - 1 6

p>\frac{10}{2}, p

p > 5, p < -8

Dvinal [7]3 years ago
3 0

Answer:

p > 5 and p <-8

Step-by-step explanation:

To solve this, you first need to isolate p.

First add 6 on both sides of the equation:

-6 + |2p+3| >7\\\\(+6) -6 + |2p+3| >7 +6\\\\2p + 3 > 13

Then subtract 3 from both sides of the equation.

2p+3-3>13-3\\\\2p > 10\\

The divide both sides by 2.

\dfrac{2p}{2}>\dfrac{10}{2}\\\\p>5

Another solution is possible because of the absolute value.

If |2p+3|>13

Then |2p+3|

<em>Thus we can solve the second solution:</em>

|2p+3|

2p+3

Isolate P again by subtracting both sides by 3

2p+3-3

2p

Then divide both sides by 2:

\dfrac{2p}{2}

p

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Solve 10 + 6(–9 – 4x) = 10(x – 12) + 8.
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10 - 54 - 24x = 10x - 120 + 8

<em>then, we just calculate that out.</em>

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<em>next, we move the terms.</em>

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Quadrilateral LMNO is similar to quadrilateral PQRS. Find the measure of side QR.
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Answer:

The measure of the side QR is 8.8.

Step-by-step explanation:

Since LMNO \sim PQRS, then SP \propto OL, RS \propto ON, RQ \propto MN and QP \propto LM. From figure we have the following relationship:

k = \frac{OL}{SP} = \frac{ON}{RS} = \frac{MN}{QR} = \frac{ML}{QP} (1)

Where k is the proportionality ratio.

If we know that SP = 13, OL = 55, MN = 37, then the measure of side QR is:

k = \frac{OL}{SP} (1b)

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The measure of the side QR is 8.8.

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