Question

Write and graph the inequality---- Please show a graph if possable.Question:A number t is less than -1 or greater than or equal to 4.

Answer 1

We will investigate how to interpret a statement and translate it into an inequality. Then we will go ahead with a plot to represent the inequality.

We are given the following statement:

`A\text{ number t is less than -1 or greater than or equal to 4}`

We see that we are looking at a one dimensional inequality i.e the inequality involves a single variable " A number t ".

We will develop an inequality to express the domain of the variable ( t ) by looking for certain keywords in the statement given. The general inequality translation rules are employed:

`\begin{gathered} t\text{ > : t is greater than} \\ t\text{ }\ge\colon\text{ t is greater than and equal to} \\ t\text{ < : t is less than} \\ t\leq\colon\text{ t is less then and equal to} \end{gathered}`

We wil use the above rules and translate the given statement into a mathematical inequality:

`t\text{ < -1 OR t }\ge\text{ 4}`

We can plot the above inequality as a one dimensional number line as follows:

Each box represents a magnitude of one unit!

The right open circle should be filled due to the equal to " = " sign!