Chapter 1.5, Problem 29PPSE

Solution

Whether the inequality $6x-13<6\left(x-2\right)$ is always, sometimes, or never true?

Always True

Given:

The inequality, $6x-13<6\left(x-2\right)$ .

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 given inequality $6x-13<6\left(x-2\right)$ , perform the basic algebraic operations to isolate the variable term as shown below

  $\begin{array}{c}6x-13<6\left(x-2\right)\\ 6x-13<6x-12\\ 6x-6x-13<6x-6x-12\\ -13<-12\end{array}$

Since the result is a true statement, the given inequality is always true.