Question

5-33. evaluate the following expressions using the order of operations.
a. $3(8 - 4)+42-(2 + 3)$ b. $7\cdot4 - 3\cdot8 + 22 - 6$ c. $7-(-3)+(-4 + 3)$ d. $-6 - 4(3\cdot2)+52$

Explanation:

Part a: \( 3(8 - 4) + 42 - (2 + 3) \)

Step 1: Simplify parentheses

First, simplify the expressions inside the parentheses. For \( 8 - 4 \), we get \( 4 \), and for \( 2 + 3 \), we get \( 5 \).
\( 3(4) + 42 - 5 \)

Step 2: Perform multiplication

Next, perform the multiplication. \( 3 \times 4 = 12 \).
\( 12 + 42 - 5 \)

Step 3: Perform addition and subtraction from left to right

First, add \( 12 \) and \( 42 \): \( 12 + 42 = 54 \). Then subtract \( 5 \): \( 54 - 5 = 49 \).

Step 1: Perform multiplications

First, perform the multiplications. \( 7 \times 4 = 28 \) and \( 3 \times 8 = 24 \).
\( 28 - 24 + 22 - 6 \)

Step 2: Perform addition and subtraction from left to right

First, subtract \( 24 \) from \( 28 \): \( 28 - 24 = 4 \). Then add \( 22 \): \( 4 + 22 = 26 \). Then subtract \( 6 \): \( 26 - 6 = 20 \).

Step 1: Simplify parentheses and double negatives

First, simplify the expression inside the parentheses: \( -4 + 3 = -1 \). Also, \( 7 - (-3) \) becomes \( 7 + 3 \) (since subtracting a negative is adding the positive).
\( 7 + 3 + (-1) \)

Step 2: Perform addition and subtraction from left to right

First, add \( 7 \) and \( 3 \): \( 7 + 3 = 10 \). Then add \( -1 \): \( 10 + (-1) = 9 \).

Answer:

\( 49 \)

Part b: \( 7 \cdot 4 - 3 \cdot 8 + 22 - 6 \)