How do you solve 1/3x + 2 >3 and -3x > 12?

Sep 19, 2016

$3 < x < 4$

Explanation:

Treat inequalities the same as equations, except if you multiply or divide by a negative value, in which case the inequality sign changes around.

$\frac{1}{3} x + 2 > 3 \textcolor{w h i t e}{\times \times \times \times \times \times \times} - 3 x > 12$

$\frac{1}{3} x > 1 \text{ "larr xx 3color(white)(xxxxxxxxxxx) 12>3x" } \leftarrow \div 3$

$x > 3 \textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times \times \times} 4 > x$

Combine the two inequalities,

$3 < x \mathmr{and} x < 4$

$\therefore 3 < x < 4$