Can I please get some help on these questions:

Question

1. If , find the value of 2 square root of 17-x = 2x-10, find the value of x/4.

2. If absolute value of 3x+6 < 9, then which of the following is a possible value of x ?
My answer choices are -7, 1, -5, -1, 10. When I solve for x, I get x<1, so can't it be -7, -5, OR -1?

3. If 5<absolute value of 2x+1<11, then which of the following is a possible value of x ?
I get 2<x<5, My answer choices are -6, -4, 2, -3, and 5.

4. If y is inversely proportional to x and y = 8 when x = 1.55, what is the value of x when y = -0.62?
I'm not sure on this

5. Simplify the following expression: 41abc(-1 + z)-41abcz
...

Thanks to anyone who can help me!

Answer 1

#1 is worded wrong, if 2 square root of 17-x = 2x-10, find the value of x/4.

Answer 2

#1 Can't quite parse the problem, but if
2√(17-x) = 2x-10
√(17-x) = x - 5
17-x = x^2 - 10x + 25
x^2 - 9x + 8 = 0
(x-1)(x-8) = 0
x = 1 or 8
but x=1 does not fit the original equation, so x=8, and x/4 = 2

#2 Recall that |n| = n if n>=0 and -n if n<0

|3x+6|<9
if 3x+6>=0, then
3x+6 < 9
x < 1

If 3x+6 < 0,
-(3x+6) < 9
-3x - 6 < 9
-3x < 15
x > -5

so -5 < x < 1
Looks like -1 is the only choice.

Think of the graph of |x|. It is a V-shape. So, if |x| < n you get the pointy part of the v below the line y=n.

#3
5 < |2x+1| < 11
This is just a sneaky way of getting you to solve two inequalities in one problem. You end up with

-6 < x < -3 or 2 < x < 5
Looks like -4 is the only choice.

#4
y = k/x
8 = k/1.55
k = 12.4
so, when y = -.62
-.62 = 12.4/x
x = -20

#5
41abc(-1 + z)-41abcz
ever heard of the distributive property?
41abc(-1) + 41abc(z) - 41abcz
-41abc + 41abcz - 41abcz
-41abc

Answer 3

Thank you!