Q54. - Algebra 2

Question

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

 

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

Step-by-Step Solution

Answer

n cold be values except option D that is 2.

Step 1 - Define the variable.

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

Step 2 - State the inequality.

The inequality is:

 

$4-5n\ge -1$

Step 3 - 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,  $n\le 1$.

Step 4 - 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).