Chapter A.9, Problem 66AYU

To determine

To solve: Each inequality. Express your answer using set notation or interval notation. Graph the solution set.

Answer to Problem 66AYU

$\left\{x|x > -\frac{7}{4}\right\}$ or $\left(-\frac{7}{4}, \infty \right)$

Explanation of Solution

Given:

$3x + 4 > \frac{1}{3\left(x - 2\right)}$

Calculation:

$3x + 4 > \frac{1}{3\left(x - 2\right)}$

Multiply by 3

$9x + 12 > \left(x - 2\right)$

$9x + 12 - 12 > x - 2 - 12$   -----(Subtract $12$ on both sides)

$9x > x - 14$

$9x - x > x - 14 - x$   -----(Subtract $x$ on both sides)

$8x > - 14$

$\frac{8x}{8} > - \frac{14}{8}$   -----(Divide $8$ on both sides)

$x > - \frac{7}{4}$

The solution set is $\left\{x|x > - \frac{7}{4}\right\}$ or using interval notation, all numbers in the interval $\left(- \frac{7}{4}, \infty \right)$