Question

1. evaluate expressions (show work)

a. evaluate: $7 + 3(2^2 - 6)$
b. evaluate: $12 - 54 - (3 + 1)$

Explanation:

Part A

Step1: Calculate the exponent

First, we calculate the exponent in the expression \(7 + 3(2^{2}-6)\). The exponent \(2^{2}\) is equal to \(4\). So the expression becomes \(7 + 3(4 - 6)\).

Step2: Simplify the parentheses

Next, we simplify the expression inside the parentheses: \(4 - 6=-2\). Now the expression is \(7 + 3(-2)\).

Step3: Multiply

Then, we perform the multiplication: \(3\times(-2)=-6\). The expression now is \(7+(-6)\).

Step4: Add

Finally, we add the two numbers: \(7+(-6) = 1\).

Step1: Simplify the innermost parentheses

First, we simplify the innermost parentheses in the expression \(12 - 5[4-(3 + 1)]\). The expression inside the innermost parentheses is \(3 + 1 = 4\). So the expression becomes \(12 - 5[4 - 4]\).

Step2: Simplify the brackets

Next, we simplify the expression inside the brackets: \(4-4 = 0\). Now the expression is \(12-5\times0\).

Step3: Multiply

Then, we perform the multiplication: \(5\times0 = 0\). The expression now is \(12-0\).

Step4: Subtract

Finally, we subtract: \(12 - 0=12\).

Answer:

\(1\)

Part B