Chapter 1.5, Problem 7LC

Solution

To describe how the properties of inequality are similar to the properties of equality and how they differ.

Given:

The specification for a length x is 43.6 cm with a tolerance of 0.1 cm.

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$, then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$, then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.

Calculation:

In order to solve the equation or inequality, we isolate the variable term on one side by performing the basic algebraic operations.

The reverse operations of addition and subtraction work similar in both solving equations and inequalities.

But the reverse operations of multiplication and division work differently for solving an equation and solving the inequality.

While multiplying or dividing the variable term with a negative number, the inequality symbol gets reverse.