## Intermediate Algebra (6th Edition)

$x=\frac{21}{4}$
We are given the equation $\frac{x}{3}+7=\frac{5x}{3}$. Then equation is then incorrectly simplified to $x+7=5x$. In order to eliminate the fractions, we must multiply all terms by 3, not just the terms with fractions. $x+21=5x$ In order to simplify the equation from here, we can subtract x from both sides. $21=4x$ Divide both sides by 4. $x=\frac{21}{4}$ Note: The equation is also incorrectly simplified after $7=4x$. Dividing both sides of this equation would result in $x=\frac{7}{4}$.