Chapter 3.6, Problem 21PPE

To determine

To find: The solution of compound inequality and graph the solution.

Answer to Problem 21PPE

The graph of solution set $y\le -2\text{ and }y\ge 5$ is:

Explanation of Solution

Given:

  $5y+7\le -3\text{ and }3y-2\ge 13$ .

Concept used:

The difference is that a solution to the inequality is not the drawn line but area of the coordinate plane that satisfy the inequality.

The common area is the solution of inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ .

A compound inequality is a combination of two or more inequalities joined by either an “and” or an “or”. In mathematics, most often it deals with equalities two statements that must, at all times, remain exactly equal to each other, however, sometimes interested in more than or less than relationship.

There is a statement and one must always be either bigger than or at least as big as the other.

Calculation:

A solution of a compound inequality involving and is any number that makes both inequalities true.

The given inequalities are:

  $5y+7\le -3\text{ and }3y-2\ge 13$ .

Solve each inequality separately to solve an inequality, it must isolate the variable on one side of the inequality symbol.

  $\begin{array}{l}5y+7\le -3.\\ 5y\le -3-7.\\ y\le -2.\end{array}$

Another inequality is:

  $\begin{array}{l}3y-2\ge 13.\\ 3y\ge 15.\\ y\ge 5.\end{array}$

Combining both the inequalities:

The solution is:

  $y\le -2\text{ and }y\ge 5$ .

To graph the solution, draw a number line and indicate the solution on it.

Hence, the graph of solution set $y\le -2\text{ and }y\ge 5$ is: