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# Please help asap!

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Please help asap!  Apr 23, 2018

### 15+0 Answers

#1
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41. |3x+6|-8=-2

3x+6-8=-2 so 3x-2=-2

x=0- one solution

and -4, (B)

Apr 23, 2018
#2
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44. Apply complex arithmetic rule, to get 38-9i, (A)

Apr 23, 2018
#3
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43. $$x\leq -4$$ or $$x \geq 3$$

.
Apr 23, 2018
#4
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please explain each of them thoroughly

Apr 23, 2018
#7
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I'll start off with 44.

Apply complex arithmetic rule: (a+bi)(c+di)=(ac-bd)(ad+bc)i

a=4, b=3, c=5, d=-6

Plugging them in, we have:

(4*5-3(-6))+(4(-6)+3*5)i

So, simplifying, we get $$38-9i$$

.
Apr 23, 2018
#9
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Please help asap!  Apr 23, 2018
#11
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41. First add 8 to both sides, to get,  |3x+6|=6

Then, we have, |f(x)|=a - f(x)=-a or f(x)=a

So, 3x+6=-6 or 3x+6=6

3x+6=-6: x=-4

3x+6=6: x=0

So, x=-4, or x=0

Apr 23, 2018
#12
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Number 41.  Apr 23, 2018
#13
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Same thing as we did in 41.

Add 2 to both sides, to get, $$|2x+1|\geq7$$

|f(x)| greater than or equal to a, f(x) less than or equal to a, or f(x) greater than or equal to a

$$2x+1\leq-7: x\leq-4$$

$$2x+1\geq7: x\geq3$$

Combine the ranges, to get $$x\leq-4$$ or $$x\geq3$$  Apr 23, 2018
#14
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Ty so so much tertre and Omi! Now I need help understanding 40 and 42 lol

Apr 23, 2018
#15
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Welcome! Solving them right now!  tertre  Apr 23, 2018
#16
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Ty I really appreciate your help!

RainbowPanda  Apr 23, 2018
#17
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Is it https://www.desmos.com/calculator/tfl8wyadtm

Apr 23, 2018
edited by tertre  Apr 23, 2018
#18
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That's how I got 42 but idk about 40

RainbowPanda  Apr 23, 2018
#19
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Nvm, I got 40 thanks everyone ^-^

Apr 23, 2018