To find the value of \( x \) in the equation, we first need to set up the equation based on the given information:
"The sum of 6 and one third of \( x \) is one more than twice \( x \)."
Let's translate this sentence into an equation:
\[ 6 + \frac{1}{3}x = 2x + 1 \]
Now, let's solve for \( x \).
1. Start by getting rid of the fraction. Multiply every term by 3 to eliminate the fraction:
\[ 3 \left( 6 + \frac{1}{3}x \right) = 3 \left( 2x + 1 \right) \]
This simplifies to:
\[ 18 + x = 6x + 3 \]
2. Next, isolate \( x \). Start by subtracting \( x \) from both sides:
\[ 18 = 5x + 3 \]
3. Subtract 3 from both sides to isolate the term with \( x \):
\[ 15 = 5x \]
4. Finally, divide both sides by 5 to solve for \( x \):
\[ x = 3 \]
So, the solution is \( x = 3 \).
The sum of 6 and one third of x is one more than twice x , find x
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