## Elementary Algebra

$\frac{1}{2}$ + $\frac{1}{3}$ $\lt$ $\frac{1}{3}$ + $\frac{1}{4}$ To check whether this inequality is true or false, we simplify it. We need to make the denominators the same in order to simplify this inequality. $\frac{1}{2}$ $\times$ $\frac{6}{6}$ + $\frac{1}{3}$ $\times$ $\frac{4}{4}$ $\lt$ $\frac{1}{3}$ $\times$ $\frac{4}{4}$ + $\frac{1}{4}$ $\times$ $\frac{3}{3}$ $\frac{6}{12}$ + $\frac{4}{12}$ $\lt$ $\frac{4}{12}$ + $\frac{3}{12}$ $\frac{10}{12}$ $\lt$ $\frac{7}{12}$ Multiply both sides by 12. 10 $\lt$ 7 Because 10 is not less than 7, this inequality is false.