Solve: 3+[5·4-(9·1+3)]-8 Using Order of Operations

Solve the following problem:

$3+[5\cdot4-(9\cdot1+3)]-8=$

Proceed to simplify the given expression whilst following the order of operations. The order of operations states that exponents precede multiplication and division, which in turn precede addition and subtraction, and that parentheses precede all of the above.

Therefore, we'll start by simplifying the expressions inside of the parentheses. In this problem, there are parentheses within parentheses, hence we'll first deal with the inner parentheses. Simplify the expression within them and continue in the same way with the outer parentheses simplifying the expression within them. We'll do all of the above while maintaining the order of operations mentioned at the beginning of the solution:

$3+[5\cdot4-(9\cdot1+3)]-8= \\ 3+[5\cdot4-(9+3)]-8= \\ 3+[5\cdot4-12]-8= \\ 3+[20-12]-8= \\ 3+8-8= \\ 3$

Given that multiplication and division precede addition and subtraction, we first performed the multiplication in the inner parentheses and then performed the addition. We continued in this way with the expression that we obtained after opening these parentheses which was in the outer parentheses. First we performed the multiplication in the first term in the outer parentheses, and then the subtraction within them, finally, after opening the outer parentheses we performed the addition and subtraction operations,

Therefore answer C is the correct answer.