Question18. Is the absolute value of -14 equal to 14? True or False.
19. What is the value of $-3+(-14)$ ? a) 11, b) -11, c) -17, d) -42

Studdy Solution

STEP 1

Assumptions
1. The absolute value of a number is the non-negative value of the number without regard to its sign.
2. Addition of negative numbers follows the rule that adding a negative number is the same as subtracting its absolute value.

STEP 2

Evaluate the absolute value of -14.
$|\,-14\,|$

STEP 3

Apply the definition of absolute value.
$|\,-14\,| = 14$

STEP 4

Determine the truth value of the statement "The absolute value of -14 is 14."
Since the absolute value of -14 is indeed 14, the statement is True.

STEP 5

Now, we will address the second problem, which involves adding two negative numbers: -3 and -14.
$-3 + (-14)$

STEP 6

Understand that adding two negative numbers is equivalent to adding their absolute values and then applying a negative sign to the result.

STEP 7

Add the absolute values of -3 and -14.
$3 + 14$

STEP 8

Calculate the sum of the absolute values.
$3 + 14 = 17$

STEP 9

Apply the negative sign to the result of the addition of the absolute values.
$-17$

STEP 10

Conclude that the sum of -3 and -14 is -17.
$-3 + (-14) = -17$
Therefore, the correct answer to problem 19 is c. -17.

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Question18. Is the absolute value of -14 equal to 14? True or False.
19. What is the value of $-3+(-14)$ ? a) 11, b) -11, c) -17, d) -42

Studdy Solution

STEP 1

Assumptions
1. The absolute value of a number is the non-negative value of the number without regard to its sign.
2. Addition of negative numbers follows the rule that adding a negative number is the same as subtracting its absolute value.

STEP 2

Evaluate the absolute value of -14.
$|\,-14\,|$

STEP 3

Apply the definition of absolute value.
$|\,-14\,| = 14$

STEP 4

Determine the truth value of the statement "The absolute value of -14 is 14."
Since the absolute value of -14 is indeed 14, the statement is True.

STEP 5

Now, we will address the second problem, which involves adding two negative numbers: -3 and -14.
$-3 + (-14)$

STEP 6

Understand that adding two negative numbers is equivalent to adding their absolute values and then applying a negative sign to the result.

STEP 7

Add the absolute values of -3 and -14.
$3 + 14$

STEP 8

Calculate the sum of the absolute values.
$3 + 14 = 17$

STEP 9

Apply the negative sign to the result of the addition of the absolute values.
$-17$

STEP 10

Conclude that the sum of -3 and -14 is -17.
$-3 + (-14) = -17$
Therefore, the correct answer to problem 19 is c. -17.

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Question18. Is the absolute value of -14 equal to 14? True or False.19. What is the value of −3+(−14)-3+(-14)−3+(−14)? a) 11, b) -11, c) -17, d) -42

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is the non-negative value of the number without regard to its sign.2. Addition of negative numbers follows the rule that adding a negative number is the same as subtracting its absolute value.

STEP 2

Evaluate the absolute value of -14.∣ −14 ∣|\,-14\,|∣−14∣

STEP 3

Apply the definition of absolute value.∣ −14 ∣=14|\,-14\,| = 14∣−14∣=14

STEP 4

Determine the truth value of the statement "The absolute value of -14 is 14."Since the absolute value of -14 is indeed 14, the statement is True.

STEP 5

Now, we will address the second problem, which involves adding two negative numbers: -3 and -14.−3+(−14)-3 + (-14)−3+(−14)

STEP 6

Understand that adding two negative numbers is equivalent to adding their absolute values and then applying a negative sign to the result.

STEP 7

Add the absolute values of -3 and -14.3+143 + 143+14

STEP 8

Calculate the sum of the absolute values.3+14=173 + 14 = 173+14=17

STEP 9

Apply the negative sign to the result of the addition of the absolute values.−17-17−17

STEP 10

Conclude that the sum of -3 and -14 is -17.−3+(−14)=−17-3 + (-14) = -17−3+(−14)=−17Therefore, the correct answer to problem 19 is c. -17.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question18. Is the absolute value of -14 equal to 14? True or False.
19. What is the value of $-3+(-14)$ ? a) 11, b) -11, c) -17, d) -42

Assumptions
1. The absolute value of a number is the non-negative value of the number without regard to its sign.
2. Addition of negative numbers follows the rule that adding a negative number is the same as subtracting its absolute value.

Evaluate the absolute value of -14.
$|\,-14\,|$

Apply the definition of absolute value.
$|\,-14\,| = 14$

Determine the truth value of the statement "The absolute value of -14 is 14."
Since the absolute value of -14 is indeed 14, the statement is True.

Now, we will address the second problem, which involves adding two negative numbers: -3 and -14.
$-3 + (-14)$

Add the absolute values of -3 and -14.
$3 + 14$

Calculate the sum of the absolute values.
$3 + 14 = 17$

Apply the negative sign to the result of the addition of the absolute values.
$-17$

Conclude that the sum of -3 and -14 is -17.
$-3 + (-14) = -17$
Therefore, the correct answer to problem 19 is c. -17.