Introductory Algebra for College Students (7th Edition)

$$x = 20$$ We check our work by plugging $20$ into the original equation to see if both sides equal one another. $$\frac{20}{4} - \frac{20}{5} = 1$$ We simplify the fractions to get: $$5 - 4 = 1$$ $$1 = 1$$ Both sides equal one another, so we know the solution is correct.
To solve this equation, we need to get rid of the fractions. To do that, we find the least common denominator of each fraction. We also can change the whole number $1$ into a fraction as well to be able to work with it easily. The lowest common denominator for this problem would be $20$. So we rewrite the fractions in this problem to get: $$\frac{5x}{20} - \frac{4x}{20} = \frac{20}{20}$$ Now we can multiply all terms by $20$ to get an equation that has no fractions: $$5x - 4x = 20$$ We combine terms to get: $$x = 20$$ We check our work by plugging $20$ into the original equation to see if both sides equal one another. $$\frac{20}{4} - \frac{20}{5} = 1$$ We simplify the fractions to get: $$5 - 4 = 1$$ $$1 = 1$$ Both sides equal one another, so we know the solution is correct.