Six less than a number equals to two. What is the number?
The Correct Answer and Explanation is :
Let’s define the unknown number as x.
According to the problem, six less than a number equals two. This can be written as the equation:
[
x – 6 = 2
]
Step 1: Solve for ( x )
To isolate ( x ), add 6 to both sides of the equation:
[
x – 6 + 6 = 2 + 6
]
[
x = 8
]
Thus, the number is 8.
Explanation:
This is a simple algebraic equation that follows the basic principles of solving for an unknown variable. Let’s break it down in detail:
- Understanding the Problem Statement
- “Six less than a number” means that we are subtracting 6 from some unknown number ( x ).
- “Equals two” tells us that the result of this subtraction is 2.
- Forming the Equation
- We translate the words into mathematical symbols:
( x – 6 = 2 ).
- Solving the Equation
- To find ( x ), we perform the opposite operation of subtraction (which is addition).
- Adding 6 to both sides cancels out the (-6) on the left, leaving us with ( x = 8 ).
- Verification
- Plugging ( x = 8 ) back into the original statement:
( 8 – 6 = 2 ), which is correct.
- Conclusion
- The value of the number is 8.
This equation is an example of a simple one-step algebraic equation, which is fundamental in problem-solving. It teaches the importance of inverse operations (addition cancels out subtraction, multiplication cancels out division, etc.).
Now, let’s generate an image illustrating the equation visually.
I’ve generated an image illustrating the equation visually. It shows a balance scale with ‘x’ on one side and ‘2 + 6’ on the other, representing the equation ( x – 6 = 2 ). The background includes a classroom blackboard with basic algebra. Let me know if you need any modifications!