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denis23 [38]

3 years ago

|2x + 2| + 7 \geqslant - 3" alt=" - 5 |2x + 2| + 7 \geqslant - 3" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

blagie [28]3 years ago

5 0

Answer:

The inequality that comes from this equation is -2 < x < 0

Step-by-step explanation:

In order to solve this equation, we need to start by solving for the absolute value portion of the equation.

-5l2x + 2l + 7 > -3

-5l2x + 2l > -10

l2x + 2l < 2

Now we need to split the equation into two different portions. One with the absolute value symbol taken away. Then we do it again with the symbol flipped and the answer negated.

2x + 2 < 2

2x < 0

x < 0

And the negated version.

2x + 2 > -2

2x > -4

x > -2

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1. x = +/- 2 $\sqrt{2}$ - 7

2. x = $3$ +/- $2i\sqrt{3}$

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Step-by-step explanation:

1. Divide both sides by 2: (x + 7)^2 = 8

Square root both sides: x + 7 = +/- 2 $\sqrt{2}$

Subtract 7 from both sides: x = +/- 2 $\sqrt{2}$ - 7

2. Square root both sides: x - 3 = $\sqrt{-12}$

Since there is a negative inside the radical, we need to have an imaginary number: $i=\sqrt{-1}$ . So, $\sqrt{-12} =i\sqrt{12} =2i\sqrt{3}$

Add 3 to both sides: x = $3$ +/- $2i\sqrt{3}$

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Square root both sides: n - 2 = $\sqrt{-2}$

Again, we have to use i: $n-2=\sqrt{-2} =i\sqrt{2}$

Add 2 to both sides: n = $2$ +/- $i\sqrt{2}$

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