Question

4-31. simplify each expression. homework help

a. $-3 + 7$
b. $7 + (-8)$
c. $-6 - 9$
d. $-3 + 4(-2)$
e. $4 - 2(-5)$
f. $(-7 + 3)(4 - 5\cdot2)$

Explanation:

Part a: $-3 + 7$

Step1: Add the numbers

We have a negative number and a positive number. To add them, we subtract the absolute values and take the sign of the number with the larger absolute value. The absolute value of $-3$ is $3$, and the absolute value of $7$ is $7$. Since $7>3$, we subtract $3$ from $7$.
$ -3 + 7 = 7 - 3 $

Step2: Calculate the result

$7 - 3 = 4$

Step1: Rewrite the addition of a negative

Adding a negative number is the same as subtracting its absolute value. So $7+(-8)$ is equivalent to $7 - 8$.
$7+(-8)=7 - 8$

Step2: Calculate the result

$7 - 8=-1$

Step1: Rewrite the subtraction

Subtracting a number is the same as adding its negative. So $-6 - 9$ is equivalent to $-6+(-9)$.

Step2: Add the negative numbers

When adding two negative numbers, we add their absolute values and keep the negative sign. The absolute value of $-6$ is $6$, and the absolute value of $-9$ is $9$. So $6 + 9 = 15$, and we keep the negative sign.
$-6+(-9)=-(6 + 9)=-15$

Answer:

$4$

Part b: $7 + (-8)$