Answer
False
Work Step by Step
$\frac{2}{3}$ - $\frac{3}{4}$ + $\frac{1}{6}$ $\gt$ $\frac{1}{5}$ + $\frac{3}{4}$ - $\frac{7}{10}$
Firstly, we need to find the least common multiple (LCM) of 3, 4, 5, 6, and 10 through each number's prime factors.
$3 = 3$
$4 = 2^{2}$
$5 = 5$
$6 = 2 \times 3$
$10 = 2 \times 5$
$LCM = 2^{2} \times 3 \times 5 = 60$
Now that we know the LCM, we can multiply the fractions by 1 such that all the denominators will be equal to 60 but the value of the each fraction does not change.
$(\frac{2}{3}$ $\times$ $\frac{20}{20}$) - ($\frac{3}{4}$ $\times$ $\frac{15}{15}$) + ($\frac{1}{6}$ $\times$ $\frac{10}{10}$) $\gt$ $(\frac{1}{5}$ $\times$ $\frac{12}{12}$) + ($\frac{3}{4}$ $\times$ $\frac{15}{15}$) - ($\frac{7}{10}$ $\times$ $\frac{6}{6}$)
$\frac{40}{60}$ - $\frac{45}{60}$ + $\frac{10}{60}$ $\gt$ $\frac{12}{60}$ + $\frac{45}{60}$ - $\frac{42}{60}$
$\frac{5}{60}$ $\gt$ $\frac{15}{60}$
Because the denominators are both 60, we can look the numerators and see that 5 is not bigger than 15, so the inequality is false.
