Translate the sentence into an equation. Twice the difference of a number and 6 is 7. Use the variable w for the unknown number.
Answer (2)
Express the difference between the number w and 6 as w − 6 .
Multiply the difference by 2: 2 ( w − 6 ) .
Set the result equal to 7: 2 ( w − 6 ) = 7 .
The equation is 2 ( w − 6 ) = 7 .
Explanation
Understanding the Sentence Let's break down the sentence step by step to translate it into an equation. The sentence is "Twice the difference of a number and 6 is 7." We'll use the variable 'w' to represent the unknown number.
Expressing the Difference First, we need to express "the difference of a number and 6". Since 'w' represents the number, this difference can be written as w − 6 .
Multiplying by Two Next, the sentence says "twice the difference". This means we need to multiply the difference we found in the previous step by 2. So, we have 2 ( w − 6 ) .
Forming the Equation Finally, the sentence says "is 7". This means the expression we found in the previous step is equal to 7. Therefore, the equation is 2 ( w − 6 ) = 7 .
Final Answer So, the equation that represents the sentence "Twice the difference of a number and 6 is 7" using the variable 'w' is 2 ( w − 6 ) = 7 .
Examples
Imagine you're trying to figure out a secret number. Someone tells you, "If you subtract 6 from my number and then double the result, you'll get 7." Translating this into an equation helps you solve for that secret number. This kind of problem is useful in many situations, like figuring out discounts or calculating how much something costs after a series of changes. For example, if a store offers a discount of $6 on an item and then doubles the discounted price, and the final price is $7, you can use this equation to find the original price of the item.
The equation that represents the sentence "Twice the difference of a number and 6 is 7" is 2 ( w − 6 ) = 7 . This is derived by representing the unknown number with the variable w , calculating the difference from 6, and multiplying by 2. Finally, we set the result equal to 7 as stated in the problem.
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