Question

basic integral representations and absolute value
state the integer that best describes each.

1. 5 yard gain
2. a withdrawal of $40
3. the stock rose 8 points
4. 20 seconds before blastoff
5. a bill for $15
6. a profit of $22
7. 9° below zero
8. 125 feet below sea level
9. a bank deposit of $35
10. sea level

evaluate.

1. |-7|
2. |15|
3. |0|
4. -|5|
5. -|-3|
6. |-7| - |4|
7. |-2| + |15|
8. |9| - |-4|
9. -|-101|
10. |-17| - |17|
11. |-13| + |-3|
12. |8| - |-7|

Explanation:

Step1: Evaluate \(|-7|\)

The absolute value of a number is its distance from zero on the number line, so \(|-7| = 7\).

Step2: Evaluate \(|15|\)

The absolute value of a positive number is the number itself, so \(|15| = 15\).

Step3: Evaluate \(|0|\)

The absolute value of zero is zero, so \(|0| = 0\).

Step4: Evaluate \(-|5|\)

First find \(|5| = 5\), then apply the negative sign: \(-|5| = -5\).

Step5: Evaluate \(-|-3|\)

First find \(|-3| = 3\), then apply the negative sign: \(-|-3| = -3\).

Step6: Evaluate \(|-7| - |4|\)

Find \(|-7| = 7\) and \(|4| = 4\), then subtract: \(7 - 4 = 3\).

Step7: Evaluate \(|-2| + |15|\)

Find \(|-2| = 2\) and \(|15| = 15\), then add: \(2 + 15 = 17\).

Step8: Evaluate \(|9| - |-4|\)

Find \(|9| = 9\) and \(|-4| = 4\), then subtract: \(9 - 4 = 5\).

Step9: Evaluate \(-|-101|\)

First find \(|-101| = 101\), then apply the negative sign: \(-|-101| = -101\).

Step10: Evaluate \(|-17| - |17|\)

Find \(|-17| = 17\) and \(|17| = 17\), then subtract: \(17 - 17 = 0\).

Step11: Evaluate \(|-13| + |-3|\)

Find \(|-13| = 13\) and \(|-3| = 3\), then add: \(13 + 3 = 16\).

Step12: Evaluate \(|8| - |-7|\)

Find \(|8| = 8\) and \(|-7| = 7\), then subtract: \(8 - 7 = 1\).

For the integer description part:

Step1: 5 yard gain

A gain is positive, so the integer is \(+5\) (or \(5\)).

Step2: a withdrawal of $46

A withdrawal is a decrease, so the integer is \(-46\).

Step3: the stock rose 8 points

A rise is positive, so the integer is \(+8\) (or \(8\)).

Step4: 20 seconds before blastoff

Before blastoff is negative time relative to blastoff, so the integer is \(-20\).

Step5: a bill for $15

A bill is an expense (decrease in money), so the integer is \(-15\).

Step6: a profit of $22

A profit is positive, so the integer is \(+22\) (or \(22\)).

Step7: \(9^\circ\) below zero

Below zero is negative, so the integer is \(-9\).

Step8: 125 feet below sea level

Below sea level is negative, so the integer is \(-125\).

Step9: a bank deposit of $35

A deposit is positive, so the integer is \(+35\) (or \(35\)).

Step10: sea level

Sea level is the reference (zero), so the integer is \(0\).

Answer:

s:

Integer Description:

1. \(5\)
2. \(-46\)
3. \(8\)
4. \(-20\)
5. \(-15\)
6. \(22\)
7. \(-9\)
8. \(-125\)
9. \(35\)
10. \(0\)

Evaluate:

1. \(7\)
2. \(15\)
3. \(0\)
4. \(-5\)
5. \(-3\)
6. \(3\)
7. \(17\)
8. \(5\)
9. \(-101\)
10. \(0\)
11. \(16\)
12. \(1\)