+0

+1
331
19
+2448

Apr 23, 2018

#1
+4568
+3

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

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

x=0- one solution

and -4, (B)

Apr 23, 2018
#2
+4568
+3

44. Apply complex arithmetic rule, to get 38-9i, (A)

Apr 23, 2018
#3
+4568
+3

43. $$x\leq -4$$ or $$x \geq 3$$

.
Apr 23, 2018
#4
+2448
+2

please explain each of them thoroughly

Apr 23, 2018
#7
+4568
+3

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
+12223
+2

Apr 23, 2018
#11
+4568
+2

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
+12223
+2

Number 41.

Apr 23, 2018
#13
+4568
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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
+2448
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Ty so so much tertre and Omi! Now I need help understanding 40 and 42 lol

Apr 23, 2018
#15
+4568
+2

Welcome! Solving them right now!

tertre  Apr 23, 2018
#16
+2448
+1

Ty I really appreciate your help!

RainbowPanda  Apr 23, 2018
#17
+4568
+2

Apr 23, 2018
edited by tertre  Apr 23, 2018
#18
+2448
+2

That's how I got 42 but idk about 40

RainbowPanda  Apr 23, 2018
#19
+2448
0

Nvm, I got 40 thanks everyone ^-^

Apr 23, 2018