Question

1. which other expression has the same value as $(-14) - (-8)$? explain your reasoning.

a. $(-14) + 8$

b. $14 - (-8)$

c. $14 + (-8)$

d. $(-14) + (-8)$

Explanation:

Step1: Simplify the original expression

Recall that subtracting a negative number is equivalent to adding its positive counterpart.
$(-14) - (-8) = (-14) + 8$

Step2: Calculate the value of the original expression

$$\begin{align*} (-14) + 8 &= -(14 - 8)\\ &= -6 \end{align*}$$

Step3: Calculate values of option a

$(-14) + 8 = -6$

Step4: Calculate values of option b

$14 - (-8) = 14 + 8 = 22$

Step5: Calculate values of option c

$14 + (-8) = 14 - 8 = 6$

Step6: Calculate values of option d

$(-14) + (-8) = -(14 + 8) = -22$

Answer:

a. $(-14) + 8$
This expression matches the simplified form of the original expression $(-14) - (-8)$, and both evaluate to $-6$, so they have the same value.