Question

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

$2\le x+5<4$

Short answer

The solution set of given inequality is $-3\le x<-1$that is $x\in [-3,-1)$.

Step-by-step solution

Step-1. Determining the solution to Inequality.

$2\le x+5<4$

$2-5\le x+5-5<4-5$ (Subtract)

$-3\le x<-1$ (Simplify)

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

The solution set consists of all numbers less than –1. In other words, the solution of the inequality is in the interval$[-3,-1)$.

Step-3. Graphing the solution set.

$$\begin{gathered} -3\le x<-1 \\ x\in [-3,-1) \end{gathered}$$