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

1 answer

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 \( x = 3 \).