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Strike441 [17]
2 years ago
12

(Absolute value inequalities) 50 points! -6|4p+2|+8 > -34

Mathematics
2 answers:
Tems11 [23]2 years ago
8 0

Answer:

-  \frac{9}{4}  < p <  \frac{5}{4}

Step-by-step explanation:

1) Subtract 8 from both sides.

- 6 |4p + 2|   >  - 34 -8

2) Simplify -34 - 8 to -42.

- 6 |4p + 2|  >  - 42

3) Divide both sides by -6.

|4p + 2|  <  \frac{ - 42}{ - 6}

4) Two negative numbers makes a positive.

|4p + 2|  <  \frac{42}{6}

5) Simplify 42/6 to 7.

|4p + 2|  < 7

6) Rewrite the inequality without the absolute value.

- 7 < 4p + 2 < 7

7) Subtract 2 from the whole equation.

- 7 - 2 < 4p < 7 - 2

8) Simplify.

- 9 < 4p < 5

9) Divide the whole equation by 4.

-  \frac{9}{4}  < p <  \frac{5}{4}

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>-</u><u> </u><u>9</u><u>/</u><u>4</u><u> </u><u><</u><u> </u><u>p</u><u> </u><u><</u><u> </u><u>5</u><u>/</u><u>4</u>.

EastWind [94]2 years ago
7 0

Answer

p>5/4 or p<-9/4

Step-by-step explanation:

1. first isolate the absolute value by subtracting 8 and then dividing by -6

2. you then split the absolute value inequality into 4p+2>7 and 4p+2<-7

3. When you solve those, you get p>5/4 and p< -9/4

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___________________________________________

for  triangle ABC

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_______________________________________

for  triangle ADC

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To understand the solution we need to draw square ABCD and diagonal AC to have better visual understanding of solution.

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algol13
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