Chapter 3.4, Problem 39PPE

To determine

To Solve: The given inequality, $4-2n\le 5-n+1$ .

Answer to Problem 39PPE

  $n\ge -2$

Explanation of Solution

Given information:

  $4-2n\le 5-n+1$

Concept Used:

We use the algebra of operations by adding or subtracting variable terms on both the sides.

Also, multi-step inequality is solved by simplifying it into equivalent one step inequality.

Calculation:

As the given inequality is $4-2n\le 5-n+1$ , we solve it as follows:

Simplifying right hand side by subtracting like terms, we get

  $\begin{array}{l}4-2n\le 5-n+1\\ 4-2n\le \left(5+1\right)-n\\ 4-2n\le 6-n\end{array}$

Adding $2n$ both the sides, we get

  $\begin{array}{l}4-2n+2n\le 6-n+2n\\ 4+\left(2n-2n\right)\le 6+\left(2n-n\right)\\ 4\le 6+n\end{array}$

Subtracting $6$ from both the sides we get

  $\begin{array}{l}4-6\le 6+n-6\\ -2\le n\end{array}$