The sum of 6 and one-third of x is one more than twice x, find x

Analyze the question: We translate the words into an equation.

• "The sum of 6 and one-third of x" → 6 + x/3
• "is one more than twice x" → 2x + 1

Equation: 6 + x/3 = 2x + 1

Solve step by step:

1. Multiply every term by 3 to remove the fraction: 18 + x = 6x + 3

2. Collect like terms (move x to the right, numbers to the left): 18 − 3 = 6x − x

3. Simplify: 15 = 5x

4. Divide by 5: x = 3

Check:

• Left side: 6 + 3/3 = 6 + 1 = 7
• Right side: 2(3) + 1 = 7 ✓

Both sides are equal, so x = 3 is correct.

Tip: Whenever you see a fraction in an equation, multiply every term by the denominator to clear it first. Then always substitute your answer back to confirm. It takes just a few seconds and saves marks.