Question

What are inequality? When do we use inequalities?What type of inequalities are there? Which symbols are used for each type?Are the following expressions variable inequalities? Why?a. 13z=27b. x<0c 3x+5x>11d. y+5≤11e. 7-1>- 32

Answer 1

Inequalities are expressions that refer to non-equivalent quantities. Inequalities can express less than, more than, less than or equal to, more than or equal to.

The type of inequalities and symbols are:

`<,>,\leq,\ge`

So, there are four types of inequalities, for example:

`\begin{gathered} x<2 \\ x>2 \\ x\leq2 \\ x\ge2 \end{gathered}`

Each inequality is different from the other, this means that the symbol used represents a type of inequality.

At last, among the choices, the inequalities are

`\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \\ 7-1>-32 \end{gathered}`

However, variable inequalities mean that the inequalities must have a variable in it. So, they are:

`\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \end{gathered}`

Therefore, the variable inequalities are b, c, and d.