Select the correct answer.
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
A. -4
B. -2
C. -1
D. 1

Let x be the number.
Set up the equation: x − 6 = 5 ( x + 2 ) .
Solve for x : x = − 4 .
The number is − 4 ​ .

Explanation

Problem Analysis Let's analyze the problem. We are given a word problem that can be translated into an algebraic equation. The problem states: "The difference of a number and 6 is the same as 5 times the sum of the number and 2." Our goal is to find the number that satisfies this condition.

Setting up the Equation Let x be the number we are trying to find. We can translate the given information into an equation:


The difference of a number and 6: x − 6 The sum of the number and 2: x + 2 5 times the sum of the number and 2: 5 ( x + 2 )
Since the difference of the number and 6 is the same as 5 times the sum of the number and 2, we have the equation: x − 6 = 5 ( x + 2 )

Solving the Equation Now, we solve the equation for x . First, distribute the 5 on the right side: x − 6 = 5 x + 10 Subtract x from both sides: − 6 = 4 x + 10 Subtract 10 from both sides: − 16 = 4 x Divide both sides by 4: x = − 4

Checking the Solution To check our answer, substitute x = − 4 back into the original equation:


Left side: x − 6 = − 4 − 6 = − 10 Right side: 5 ( x + 2 ) = 5 ( − 4 + 2 ) = 5 ( − 2 ) = − 10
Since both sides are equal, our solution is correct.

Final Answer The number is -4. Therefore, the correct answer is A.

Examples
Understanding how to translate word problems into algebraic equations is a fundamental skill in mathematics. For example, suppose you are managing a budget for a school event. You know that the cost of renting the venue is a fixed amount, and you also have a per-student cost for materials. By setting up an equation that relates the number of students attending to the total cost, you can determine how many students need to attend to break even or reach a certain profit target. This involves translating the given information into an equation and solving for the unknown variable, just like in the problem we solved.

Answered by GinnyAnswer | 2025-07-03

The number that satisfies the given condition is − 4 . After solving the equation, we verified that both sides are equal, confirming the solution. Thus, the correct answer is A.
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Answered by Anonymous | 2025-07-04