Question

Please help me. I've been working on this for an hour and I just need an answer. Thank you so much if you do all of these. I will forever be indebted to you :)

Part A:

Rewrite without absolute value for the given conditions:

1) y = |x−3|+|x+2|−|x−5|, if x > 5

2) y = |10-x|, if x<10


Part B:

Write the absolute value equations in the form x−b=c (where b is a number and c can be either number or an expression) that have the following solution sets:

1) All numbers such that x≤5.

2) All numbers such that x≤−14.


Again, thank you so much if you do all of these!

Answer 1

Explanation:

Rewrite without absolute value for the given conditions:

1) y = |x−3|+|x+2|−|x−5|, if x > 5

y = x-3 + x + 2 - (x-5)

y = x + 4

2) y = |10-x|, if x<10

y = 10 - x

In both cases, the value of x is held to values that make the absolute value notation redundant, so they can be removed.

===============

Write the absolute value equations in the form x−b=c (where b is a number and c can be either number or an expression) that have the following solution sets:

I actually don't understand the question. Rewrite the above equations, or make new ones? Sorry.

1) All numbers such that x≤5

x≤5 kinda does it for me. X can be any number less than or equal to 5. Ta da. (?)

2) All numbers such that x≤−14.

x ≤ -14

Same comment. I'm not sure what is being asked.