Seven less than the product of 2 and a number is equal to 4.
The Correct Answer and Explanation is:
Correct Answer:
Let the unknown number be x.
The phrase “the product of 2 and a number” means:2x2x2x
“Seven less than the product of 2 and a number” means:2x−72x – 72x−7
This is said to be equal to 4, so the equation becomes:2x−7=42x – 7 = 42x−7=4
Solve the equation:
Step 1: Add 7 to both sides:2x−7+7=4+7⇒2x=112x – 7 + 7 = 4 + 7 \Rightarrow 2x = 112x−7+7=4+7⇒2x=11
Step 2: Divide both sides by 2:2×2=112⇒x=112\frac{2x}{2} = \frac{11}{2} \Rightarrow x = \frac{11}{2}22x=211⇒x=211
Final Answer:
x=112 or 5.5x = \frac{11}{2} \text{ or } 5.5x=211 or 5.5
Explanation
To solve the given problem, we must first understand the wording and translate it into a mathematical expression. The problem reads: “Seven less than the product of 2 and a number is equal to 4.”
The key parts of this sentence are:
- “Product of 2 and a number”: This refers to multiplication. If the unknown number is represented by x, then the product is written as 2x.
- “Seven less than”: This means we are subtracting 7 from the quantity mentioned. In algebra, “seven less than 2x” is written as 2x − 7.
- “Is equal to 4”: This tells us what the left-hand side equals. So we write 2x − 7 = 4.
Once the equation is formed, solving it becomes straightforward. The first step is to isolate the variable x. We do this by first adding 7 to both sides to cancel out the -7. This gives 2x = 11.
Next, we divide both sides by 2 to solve for x, giving x = 11/2 or 5.5.
The solution tells us that the number we were trying to find is 5.5. If we substitute x = 5.5 back into the original expression, we get 2 × 5.5 = 11, and 11 − 7 = 4, which confirms our answer is correct. This process involves translating language into algebra and then applying basic operations to solve.
