Twice a number divide by 6 is 42
The Correct Answer and Explanation is:
Answer:
Let the unknown number be xx.
The equation is: 2×6=42\frac{2x}{6} = 42
Step 1: Simplify the left side. 2×6=x3\frac{2x}{6} = \frac{x}{3}
So the equation becomes: x3=42\frac{x}{3} = 42
Step 2: Solve for xx.
Multiply both sides of the equation by 3: x=42×3=126x = 42 \times 3 = 126
Final Answer: x=126x = 126
Explanation
This problem is a classic algebraic equation that asks you to find an unknown number based on a given condition. The phrase “twice a number divided by 6 is 42” translates mathematically to: 2×6=42\frac{2x}{6} = 42
Here, “twice a number” means 2x2x, and “divided by 6” refers to dividing that expression by 6. The result of that division is 42.
To solve the equation, the first step is to simplify the fraction. 2×6\frac{2x}{6} reduces to x3\frac{x}{3} because 2 and 6 have a common factor of 2. Simplifying expressions is a useful step in algebra to make the equation easier to solve.
So now the equation is: x3=42\frac{x}{3} = 42
Next, to isolate xx, we do the opposite of division, which is multiplication. Multiplying both sides by 3 eliminates the denominator: x=42×3=126x = 42 \times 3 = 126
This means the original number is 126. We can check our answer by plugging it back into the original expression:
Twice 126 is 252.
252 divided by 6 equals 42.
So the answer is correct.
This problem demonstrates key algebra skills: translating words into math, simplifying expressions, and solving equations using inverse operations. It also highlights the importance of checking your work to confirm the solution makes sense in the original context. These fundamental strategies apply to a wide range of math problems.
