Questions: If x/7-5=x/2, evaluate x^2-x x^2-x=□ (Type an integer or a simplified fraction.)

Solution Steps

To solve the equation \(\frac{x}{7} - 5 = \frac{x}{2}\), we first need to find a common denominator to eliminate the fractions. Once the fractions are cleared, we can solve for \(x\). After finding the value of \(x\), we substitute it into the expression \(x^2 - x\) to evaluate it.

We start with the equation

\[ \frac{x}{7} - 5 = \frac{x}{2}. \]

To eliminate the fractions, we can multiply through by the least common multiple of the denominators, which is 14:

\[ 14 \left(\frac{x}{7}\right) - 14 \cdot 5 = 14 \left(\frac{x}{2}\right). \]

This simplifies to:

\[ 2x - 70 = 7x. \]

Next, we rearrange the equation to isolate \(x\):

\[ 2x - 7x = 70, \]

which simplifies to:

\[ -5x = 70. \]

Dividing both sides by -5 gives:

\[ x = -14. \]

Now that we have \(x = -14\), we substitute this value into the expression \(x^2 - x\):

\[ x^2 - x = (-14)^2 - (-14) = 196 + 14 = 210. \]

Final Answer