Chapter 3.4, Problem 20P

Solve each inequality, if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers.

$-3(w+3)<9-3w$

To determine

ToSolve:The inequality $-3\left(w+3\right)<9-3w$ , if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers.

Answer to Problem 20P

The solution of given inequality are all real numbers.

Explanation of Solution

Given:

The inequality $-3\left(w+3\right)<9-3w$

Concept Used:

The solution of aninequality is the set of all the values which satisfies the inequality.

For any real numbers $a,b$ and $c$

  $a\left(b+c\right)=ab+ac$

Calculation:

Given the inequality $-3\left(w+3\right)<9-3w$

Solving it, we have

  $\begin{array}{c}-3\left(w+3\right)<9-3w\\ \left(-3\right)\left(w\right)+\left(-3\right)\left(3\right)<9-3w\text{ Using }a\left(b+c\right)=ab+ac\\ -3w-9<9-3w\\ -3w-9+9<9-3w+9\text{ Add 9 to both sides}\end{array}$

  $\begin{array}{c}-3w<18-3w\\ -3w+3w<18-3w+3w\text{ Add }3w\text{ to both sides}\\ 0<18\text{ True}\end{array}$

Therefore, thesolution of given inequality areall real numbers.

Conclusion:

The solution of given inequality are all real numbers.