Problem 81 - Introductory Algebra for College Students

Question

If \(\frac{x}{5}-2=\frac{x}{3},\) evaluate \(x^{2}-x\)

Step-by-Step Solution

Answer

The evaluated result of \(x^{2}-x\) is 210.

Step 1: Solve for \(x\)

First, the equation \(\frac{x}{5}-2=\frac{x}{3}\) needs to be solved for \(x\). To do this, we need to eliminate fractions by multiplying each side of the equations by the least common multiple of 5 and 3 which is 15. This gives \[15\times\frac{x}{5}-15\times2=15\times\frac{x}{3}\] which simplifies to \(3x-30=5x\). Finally, rearranging the equation results in the value of \(x\), which is \(x=15\).

Step 2: Substitute \(x\) into \(x^{2}-x\)

Now that \(x\)=15 is known, it should be used to find the value of \(x^{2}-x\). Substituting 15 into the expression gives \(15^2-15\).

Step 3: Simplify the expression

The expression \(15^2-15\) simplifies to give \(225-15\) which equals to 210.