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Continuity in an Interval

log31+2x1+x<1

Question

${log}_{3} \frac{1 + 2 x}{1 + x} < 1$

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Solution

${log}_{3} \frac{1 + 2 x}{1 + x} < 1$
$\frac{1 + 2 x}{1 + x} < 3$
$1 + 2 x < 3 (1 + x)$
$2 x + 1 < 3 + 3 x$
$- x - 2 < 0$
$x + 2 > 0$
$x > - 2$

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