### Home > PC3 > Chapter 6 > Lesson 6.1.3 > Problem6-59

6-59.

Solve each of the following inequalities.

1. $\frac { x - 4 } { x - 1 } > \frac { x } { 3 } + 4$

$\frac{x-4}{x-1}-\frac{x}{3}-4>0$

$\frac{3(x-4)}{3(x-1)}-\frac{x(x-1)}{3(x-1)}-\frac{12(x-1)}{3(x-1)}>0$

$\frac{3(x-4)-x(x-1)-12(x-1)}{3(x-1)}>0$

Combine like terms in the numerator and factor. Then determine the boundary points and then the intervals that make the inequality true.

1. $x^4−14x^2+40<0$

$(x^2-10)(x^2-4)\le 0$

$(x-\sqrt{10})(x+\sqrt{10})(x-2)(x+2)\le 0$

Determine the boundary points and then the intervals that make the inequality true.