Question

lesson 2: absolute value & operations with integers
directions: solve each problem. show your work!!!

1. solve |-8|=
2. solve |10|=
3. solve -|7|=
4. solve |5 - 9| + 2·3 =
5. solve 10 - |4 - 3| + 2 =
6. true or false |9 - 12| > |1 - 6|
7. true or false |-7| > -|-7|
8. order from least to greatest 4, -5, -7
9. a submarine is 140 ft below sea level. it rose 30 ft. what integer describes the new depth of the submarine?

Explanation:

Step1: Solve absolute value

$|-8| = 8$

Step2: Solve absolute value

$|10| = 10$

Step3: Solve absolute value then apply sign

$-|7| = -7$

Step4: Compute inside absolute value first

$|5-9| = |-4| = 4$
Multiply then add: $4 + 2\cdot3 = 4 + 6 = 10$

Step5: Compute inside absolute value first

$|4-3| = |1| = 1$
Subtract then add: $10 - 1 + 2 = 11$

Step6: Compute both absolute values

$|9-12| = |-3| = 3$, $|1-6| = |-5| = 5$
Compare: $3 > 5$ is False

Step7: Compute both sides

$|-7| = 7$, $-|-7| = -7$
Compare: $7 > -7$ is True

Step8: Order negative/positive integers

Negative numbers with larger magnitude are smaller: $-7 < -5 < 4$

Step9: Calculate new depth

Initial depth: $-140$ ft, rise $30$ ft: $-140 + 30 = -110$

Answer:

1. $8$
2. $10$
3. $-7$
4. $10$
5. $11$
6. False
7. True
8. $-7, -5, 4$
9. $-110$

(Note: For the drawing components:

1. Draw the hair for answer 8
2. Draw the nose for answer 10
3. Draw "Zero is my Hero!" on the shirt for answer -7
4. Draw #'s on the sleeves for answer 10
5. Draw the first set of eyes for answer 11
6. Draw the second headpiece for False
7. Draw 0,0,0,0 on the serving tray for True
8. Draw the first chalkboard for $-7, -5, 4$
9. Write "Brahmagupta" for answer -110)