interval notation: solve -8<4-x<=12, /x-6/=10, (2+3i)(4-i)

[xtacy4u2c]

I have several questions with my college algebra.

1. Solve for x and write your answer using interval notation -8 < 4 - x <= 12? Help please

2. Solve for x: /x-6/ = 10?

3. i denotes the square root of -1
multiply and simplify (2+3i) (4-i)

 

[stapel]

What are your thoughts? What have you tried? How far did you get? Where are you stuck?

1. Solve for x... -8 < 4 - x <= 12?

You subtracted 4 from all three "sides", multiplied through to get a positive x, and... then what?

2. Solve for x: /x-6/ = 10?

For what are you using the division symbol? What operation does this represent?

3. multiply and simplify (2+3i) (4-i)

You "FOILed" the two binomials, simplified the i[sup:2flsqhzu]2[/sup:2flsqhzu] term, combined like terms, and... then what?

Please be complete. Thank you!

Eliz.

 

[fasteddie65]

1. Solve for x and write your answer using interval notation -8 < 4 - x <= 12? Help please
-8 < 4 - x < 12
Subtract 4 from all terms.
-12 < -x < 8
Divide all terms by -1.
12 > x > -8
Rearrange in increasing order.
-8 < x < 12

2. Solve for x: /x-6/ = 10?
x - 6 = 10 or x - 6 = -10
Add 6 in both equations.
x = 4 or x = -4

3. i denotes the square root of -1
multiply and simplify (2 + 3i) (4 - i) = 8 - 2i + 12i - 3i^2
But 3i^2 = -3
8 - 2i + 12i - 3i^2 = 8 + 10i - (-3) = 11 + 10i