Question

1. which expression is equivalent to 12 - 17?

a. 17 - 12
b. 12 + 17
c. 12 + (-17)
d. 12 - (-17)

1. which expression does not have a value of 3?

a. -25 - (-28)
b. 16 - 13
c. -45 - 42
d. -28 - (-31)

Explanation:

Question 4: Which expression is equivalent to \( 12 - 17 \)?

Step 1: Recall the rule of subtraction as adding the opposite

Subtracting a number is the same as adding its additive inverse. So, \( a - b = a + (-b) \). For \( 12 - 17 \), this means \( 12 + (-17) \).

Step 2: Analyze each option

• Option a: \( 17 - 12 = 5 \), while \( 12 - 17 = -5 \), so not equivalent.
• Option b: \( 12 + 17 = 29 \), not equivalent to \( -5 \).
• Option c: \( 12 + (-17) \), which matches the rule from Step 1. Let's calculate: \( 12 + (-17) = -5 \), and \( 12 - 17 = -5 \), so this is equivalent.
• Option d: \( 12 - (-17) = 12 + 17 = 29 \), not equivalent.

Step 1: Calculate each option

• Option a: \( -25 - (-28) = -25 + 28 = 3 \) (since subtracting a negative is adding the positive).
• Option b: \( 16 - 13 = 3 \).
• Option c: \( -45 - 42 = -87 \) (subtracting a positive from a negative: \( -45 - 42 = -(45 + 42) = -87 \)).
• Option d: \( -28 - (-31) = -28 + 31 = 3 \) (subtracting a negative is adding the positive).

Step 2: Identify the non - 3 value

From the calculations, Option c gives -87, which is not 3.

Answer:

c. \( 12 + (-17) \)

Question 5: Which expression does not have a value of 3?