+0  
 
+1
91
19
avatar+1164 

Please help asap!

RainbowPanda  Apr 23, 2018
 #1
avatar+2765 
+3

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

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

x=0- one solution

 

and -4, (B)

tertre  Apr 23, 2018
 #2
avatar+2765 
+3

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

tertre  Apr 23, 2018
 #3
avatar+2765 
+3

43. \(x\leq -4\) or \(x \geq 3\)

tertre  Apr 23, 2018
 #4
avatar+1164 
+2

please explain each of them thoroughly

RainbowPanda  Apr 23, 2018
 #7
avatar+2765 
+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 \(38-9i\)

tertre  Apr 23, 2018
 #9
avatar+9490 
+2

Please help asap!

 

laugh

Omi67  Apr 23, 2018
 #11
avatar+2765 
+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

tertre  Apr 23, 2018
 #12
avatar+9490 
+2

Number 41.

laugh

Omi67  Apr 23, 2018
 #13
avatar+2765 
+2

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 \(x\geq3\)

 

smileysmiley

tertre  Apr 23, 2018
 #14
avatar+1164 
+2

Ty so so much tertre and Omi! Now I need help understanding 40 and 42 lol

RainbowPanda  Apr 23, 2018
 #15
avatar+2765 
+2

Welcome! Solving them right now! smileysmiley

tertre  Apr 23, 2018
 #16
avatar+1164 
+1

Ty I really appreciate your help!

RainbowPanda  Apr 23, 2018
 #17
avatar+2765 
+2

Is it https://www.desmos.com/calculator/tfl8wyadtm

tertre  Apr 23, 2018
edited by tertre  Apr 23, 2018
 #18
avatar+1164 
+2

That's how I got 42 but idk about 40

RainbowPanda  Apr 23, 2018
 #19
avatar+1164 
0

Nvm, I got 40 thanks everyone ^-^

RainbowPanda  Apr 23, 2018

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