Chapter 5.2, Problem 43HP

(a)

To determine

Solve the inequality for x.

Answer to Problem 43HP

  $x>-\frac{5}{a}$

Explanation of Solution

Given:

The inequality equation: $-ax<5$

Concept Used:

The inequality equation: $-ax<5$

Calculation:

The inequality equation: $-ax<5$

Solve for x:

  $\begin{array}{l}-ax<5\\ \frac{-ax}{-a}>\frac{5}{-a}[\text{Divide}\text{both}\text{sides}\text{by}-a\text{and}\text{reverse}\text{the}\text{inequality}\text{]}\\ x>-\frac{5}{a}\end{array}$

Solution of $-ax<5$ is $x>-\frac{5}{a}$

Thus, solution of $-ax<5$ is $x>-\frac{5}{a}$

(b)

To determine

Solve the inequality for x.

Answer to Problem 43HP

  $x\ge 8a$

Explanation of Solution

Given:

The inequality equation: $\frac{1}{a}x\ge 8$

Concept Used:

The inequality equation: $\frac{1}{a}x\ge 8$

Calculation:

The inequality equation: $\frac{1}{a}x\ge 8$

Solve for x:

  $\begin{array}{l}\frac{1}{a}x\ge 8\\ a·\frac{1}{a}x\ge a·8\text{[}\text{Multiply}\text{both}\text{sides}\text{by}a\text{]}\\ x\ge 8a\end{array}$

Solution of $\frac{1}{a}x\ge 8$ is $x\ge 8a$

Thus, solution of $\frac{1}{a}x\ge 8$ is $x\ge 8a$

(c)

To determine

Solve the inequality for x.

Answer to Problem 43HP

  $-\frac{6}{a}\ge x$

Explanation of Solution

Given:

The inequality equation: $-6\ge ax$

Concept Used:

The inequality equation: $-6\ge ax$

Calculation:

The inequality equation: $-6\ge ax$

Solve for x:

  $\begin{array}{l}-6\ge ax\\ \frac{-6}{a}\ge \frac{ax}{a}\text{[}\text{Divide}\text{both}\text{sides}\text{by}a\text{]}\\ -\frac{6}{a}\ge x\end{array}$

Solution of $-6\ge ax$ is $-\frac{6}{a}\ge x$

Thus, solution of $-6\ge ax$ is $-\frac{6}{a}\ge x$