Q 1. - Precalculus Enhanced with Graphing Utilities

Question

Solve each inequality :

(a)$3x-7<8-2x$

(b)$x^2-x-6>0$

Step-by-Step Solution

Answer

The answer of part (a) is $x<3$

and part (b) is either $x>-2 or x<-2$.

Part (a) Step 1. Given information

Given expression is $3x-7<8-2x$

Part (a) Step 2. Solution

Adding $\text{'}2x+7\text{'}$ both sides, we have,

$$\begin{gathered} 3x-7+2x+7<8-2x+2x+7 \\ 5x<15 \\ x<3 \end{gathered}$$

Part (b) Step 1. Given information

Given expression is $x^2-x-6>0$

Part (b) Step 2. Solution

$$\begin{gathered} x^2-x-6>0 \\ (x-3)(x+2)>0 \end{gathered}$$

Either $x>3 and x>-2$this implies that  $x>-2$

or $x<3 and x<-2$ this implies that $x<-2$