Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

Solve the inequality. Graph the solution set.

$2-3x>6$

Step-by-Step Solution

Answer

The solution set of the given inequality is $\left(-\infty ,\frac{-4}{3}\right)$

The graph of the solution set is given as:

Step 1. Given information

The given inequality is $2-3x>6$

Step 2. Solve the inequality

Using properties of inequalities, we get:

$$\begin{gathered} 2-3x>6 \\ -3x>4 \\ 3x<-4 [multiply both sides by -1] \\ x<\frac{-4}{3} \end{gathered}$$

Step 3. Verify the solution

Substituting the value less than $-\frac{4}{3}$ i.e., $\frac{-5}{3}$ in the inequality, we get:

$$\begin{gathered} 2-3x>6 \\ 2-3\times -\frac{5}{3}>6 \\ 2-\left(-5\right)>6 \\ 7>6 \end{gathered}$$

This is true.

Hence the solution of the inequality is

$x<-\frac{4}{3}$

Step 4. Graph the solution set.

The graph of the solution set is given as: