# How do you solve and write the following in interval notation: 1/4x+3>=4-1/3x?

Feb 15, 2017

#### Answer:

$\left[\frac{12}{7} , + \infty\right)$

#### Explanation:

Multiply ALL terms on both sides of the inequality by 12, the LCM of 4 and 3

$\left({\cancel{12}}^{3} \times \frac{x}{\cancel{4}} ^ 1\right) + \left(12 \times 3\right) \ge \left(12 \times 4\right) - \left({\cancel{12}}^{4} \times \frac{x}{\cancel{3}} ^ 1\right)$

$\Rightarrow 3 x + 36 \ge 48 - 4 x$

collect terms in x on the left side and numeric values on the right side.

add 4x to both sides.

$3 x + 4 x + 36 \ge 48 \cancel{- 4 x} \cancel{+ 4 x}$

$\Rightarrow 7 x + 36 \ge 48$

subtract 36 from both sides.

$7 x \cancel{+ 36} \cancel{- 36} \ge 48 - 36$

$\Rightarrow 7 x \ge 12$

$\frac{\cancel{7} x}{\cancel{7}} \ge \frac{12}{7}$

$\Rightarrow x \ge \frac{12}{7} \text{ is the solution}$

$\text{expressed in interval notation } \left[\frac{12}{7} , + \infty\right)$