Chapter 3.4, Problem 1P

Solve each inequality. Check your solutions.

$3f+9<21$

To determine

ToSolve:The inequality $3f+9<21$ and check the solution.

Answer to Problem 1P

The set of solutions of the given inequality is the interval $\left(-\infty ,4\right)$

Explanation of Solution

Given:

The inequality $3f+9<21$

Concept Used:

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

Calculation:

Given the inequality $3f+9<21$

Solving it, we have

  $\begin{array}{c}3f+9<21\\ 3f+9-9<21-9\text{ Subtract 9 from both sides}\\ 3f<12\\ \frac{3f}{3}<\frac{12}{3}\text{ Divide both sides by 3}\end{array}$

  $f<4$

That is $f\in \left(-\infty ,4\right)$

Therefore, the set of solutions of the given inequality is the interval $\left(-\infty ,4\right)$

Checking

At end point $f=4$

Substituting $f=4$ into the given inequality, we have.

  $\begin{array}{c}3f+9<21\\ 3\left(4\right)+9<21\text{ Substitute }f=4\\ 12+9<21\\ 21<21\text{ Which is FALSE}\end{array}$

Substituting a solution from the set of solutions into the given inequality say $f=2$ , we have. $\begin{array}{c}3f+9<21\\ 3\left(2\right)+9<21\text{ Substitute }f=2\\ 6+9<21\\ 15<21\text{ Which is TRUE}\end{array}$

Thus, set of solutions $\left(-\infty ,4\right)$ of the given inequality is correct.

Conclusion:

The set of solutions of the given inequality is the interval $\left(-\infty ,4\right)$