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