math homework??

Question

Solve the inequality. (Use "<=" to represent "less than and equal to" and ">=" to represent "greater than and equal to".)

/9 - h/ =0


and

Solve the inequality. (Use "<=" to represent "less than and equal to" and ">=" to represent "greater than and equal to".)

11- 8/n/ > -13

Answer 1

Absolute value expressions, when isolated, can be either positive or negative. Those that are = or > are combined with an "or" statement, and those with < are combined with an "and" statement (think "greatOR" and "less thAND").

|9 - h| = 0. The abs value is isolated (by itself). It's an =, meaning it's an "or" statement.
(9 - h) = 0 or -(9 - h) = 0. Now solve each equation.
Both solve to h = 9.

11 - 8|n| > -13. Subtract 11.
-8|n| > -24. Divide by -8... remember that with an inequality, multiplying by a negative changes the inequality!
|n| < 3. The abs value is isolated. It's less than, so it's an "and" statement.
(n) < 3 and -(n) < 3. The first inequality is solved as is: n < 3. For the second, multiply both sides by a negative (and flip-flop the inequality).
n > -3.
The solution is n < 3 and n > -3, which is more neatly written
-3 < n < 3.

Answer 2

Absolute Value

|9 - h| = 0

9 - h = 0

9 - h + h = 0 + h

9 = h

- - - - - - -

11 - 8 |n| > - 13

11 - 8n > - 13

11 - 8n - 11 > - 13 - 11

- 8n > - 24

- 8n / - 8 < - 24 / - 8

n < - 24 / - 8

n < 24 / 8

n < 3

- - - - - - - -s-

Answer 3

1. 9=h
2. -8|n|>-24 or |n|<3 so -3

Answer 4

h=9

-8/n/>-24
/n/<3
n<3
n>-3

Answer 5

do your own homework!