Inequalities and Absolute Value

Solve.

3|2d + 9| + 13 > 10

• d > 5 or d < -1

• d < -4 or d > 5

• No Solution

• All real numbers

Solve.

|-3f| ≥ 6.3

• -18.9 ≤ f ≤ 18.9

• no solution

• f ≤ -2.1 or f ≥ 2.1

• -2.1 ≤ f ≤ 2.1

Solve.
|4m + 9| ≥ 21

• -7.5 ≤ m ≤ 3

• m ≤ -7.5 or m ≥ 3

• -3 ≤ m ≤ 7.5

• m ≤ -3 or m ≥ 7.5

The rules for an essay contest say that entries can have 500 words with an absolute deviation of at most 30 words. Which inequality represents represents the acceptable number of words?

• |x - 30| < 500

• |x - 30| ≤ 500

• |x - 500| < 30

• |x - 500| ≤ 30

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

Solve.
-5|x - 4| > -20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

What is the correct first step?

• divide by 10

• multiply by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and"

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• no solution

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and

• or