Answer
$(-∞,\frac{7}{5})$
Work Step by Step
$\frac{1-2x}{3} + \frac{3x+7}{7} \gt 1$
Multiply both sides by the LCD, $21$ to clear fractions.
$21(\frac{1-2x}{3} + \frac{3x+7}{7} ) \gt 21 (1)$
Applying distributive property,
$21(\frac{1-2x}{3}) +21( \frac{3x+7}{7} ) \gt 21$
$7(1-2x) +3(3x+7) \gt 21$
Applying distributive property again,
$7-14x+9x+21 \gt 21$
$-5x+28 \gt 21$
Add $-28$ on both sides.
$-5x+28-28 \gt 21-28$
$-5x \gt -7$
Divide both sides by $-5$ and reverse the inequility symbol.
$\frac{-5x}{-5} \lt \frac{-7}{-5}$
$x \lt \frac{7}{5}$
In interval notation $(-∞,\frac{7}{5})$
