Question

Solve the linear Inequality. Express the solution using interval notation and graph the solution set.

$\frac{1}{3}x+2<\frac{1}{6}x-1$

Short answer

The solution set of given inequality is$x<-18$that

is $x\in (-\infty ,-18)$.

Step-by-step solution

Step-1. Determining the solution to Inequality.

$\frac{1}{3}x+2<\frac{1}{6}x-1$

$\frac{1}{3}x-\frac{1}{6}x+2<\frac{1}{6}x-\frac{1}{6}x-1$ (Subtract $\frac{1}{6}x$)

$\frac{1}{6}x+2<-1$ (Simplify)

$\frac{1}{6}x+2-2<-1-2$ (Subtract 2)

$\frac{1}{6}x<-3$ (Simplify)

$6\times \frac{1}{6}x<-3\times 6$ (Multiply by 6)

$x<-18$ (Simplify)

Step-2. Expressing the solution set in Interval Notation.

The solution set consists of all numbers less than –18. In other words, the solution of the inequality is in the interval$(-\infty ,-18)$

Step-3. Graphing the solution set.

$$\begin{gathered} x<-18 \\ x\in (-\infty ,-18) \end{gathered}$$