Question

If $4-5\text{n}\ge -1$, then localid="1647865234189" $\text{n}$could equal all of the following except:

A. $-\frac{1}{5}$ B. $\frac{1}{5}$ C. $1$ D. $2$

Short answer

n cold be values exceptoption D that is 2.

Step-by-step solution

- Define the variable.

A variable is a term that is used to represent an unknown value.

- State the inequality.

The inequality is:

$4-5n\ge -1$

- Solve the inequality.

To simplify the inequality, use the subtraction property.

Simplify the inequality as shown below:

$\begin{array}{c}4-5n\ge -1\\ 4-5n+5n\ge -1+5n\\ 4+1\ge -1+5n+1\\ 5\ge 5n\\ 1\ge n\\ n\le 1\end{array}$

Therefore, $n\le 1$.

- State the conclusion.

As $n\le 1$.

Option A that is $-\frac{1}{5}$ is less than 1. So, $n$can take the value $-\frac{1}{5}$.

Option B that is $\frac{1}{5}$ is less than 1. So, $n$can take the value $\frac{1}{5}$.

Option C that is $1$ is equal 1. So, $n$can take the value $1$.

Option D that is $2$ is greater than 1. So, $n$cannot take the value $2$.

Therefore, $n$be equal to all the options that is (A, B, C) except option D (that is 2).