Select the correct combination of mathematical signs to replace the asterisks so that the following equation becomes true when evaluated with normal precedence rules: 48 * 4 * 6 * 3 * 30

Introduction:
This is a coded operator placement question. We are given a numerical expression with asterisks in place of arithmetic operators. A set of possible operator combinations is provided, and we must select the one that makes the equation valid when standard rules of arithmetic are followed. The equation must ultimately have an equality sign that correctly balances the left and right sides.

Given Data / Assumptions:
The expression is 48 * 4 * 6 * 3 * 30, and there are four asterisks to be replaced by operators in a fixed left to right order. Each option provides a sequence of four symbols which correspond to the first, second, third, and fourth asterisk respectively. The operators involved are addition, subtraction, multiplication, division, and equality. We assume ordinary operator precedence, where multiplication and division are performed before addition and subtraction.

Concept / Approach:
The strategy is to test each option by substituting its operators into the expression and then checking whether the resulting statement is a true numerical equation. Because there are only four options given in the original list, and the structure is not too long, we can systematically evaluate each candidate without much difficulty.

Step-by-Step Solution:
Step 1: Consider option a: -, +, =, x. Substituting gives 48 - 4 + 6 = 3 x 30. The left side is 48 - 4 + 6 = 50. The right side is 3 * 30 = 90. Since 50 is not equal to 90, option a is invalid.Step 2: Consider option b: ÷, =, x, +. Substituting gives 48 ÷ 4 = 6 x 3 + 30. The left side is 48 ÷ 4 = 12. The right side is 6 * 3 + 30 = 18 + 30 = 48. Since 12 is not equal to 48, option b is also invalid.Step 3: Consider option c: ÷, +, x, =. Substituting gives 48 ÷ 4 + 6 x 3 = 30. First compute the left side using precedence: 48 ÷ 4 = 12 and 6 x 3 = 18, so the left side becomes 12 + 18 = 30.Step 4: With option c, the equation is 30 = 30, which is a true statement. Therefore option c balances the equation correctly.Step 5: For completeness, option d gives 48 - 4 = 6 x 3 + 30 which becomes 44 = 48, clearly false, and option e also fails to balance the equation when evaluated.

Verification / Alternative check:
We can directly see that 48 ÷ 4 = 12 and 6 x 3 = 18, and these two quantities sum to 30, matching the right side. There is no other straightforward combination among the options that yields such a neat equality.

Why Other Options Are Wrong:
Each incorrect option generates a left side and right side that do not match. They either make the left side smaller or larger than the right side, or produce an equation that is obviously unbalanced. None of them produce the required 30 on both sides at the same time.

Common Pitfalls:
One common mistake is to ignore operator precedence and evaluate strictly left to right, which would produce different values and potentially mislead you into thinking an incorrect option is correct. Another error is to misread the mapping of operators to asterisks and put them in the wrong positions.

Final Answer:
The correct sequence of operators is ÷, +, x, =, corresponding to option c.