Chapter 8.6, Problem 20IP

To determine

Find for the given value, state whether the inequality $4.5b\ge -12;b=-4$ is true or false.

Answer to Problem 20IP

False

Explanation of Solution

Given:

The Inequality: $4.5b\ge -12;b=-4$

Concept Used:

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b.

There are four different types of inequalities:

Greater than − $(>)$ ; Less than − $(<)$ ; Greater than or equal to − $(\ge )$ ; Less than or equal to − $(\le )$

For Inequality equation: If $b>c\Rightarrow c<b\text{or}b<c\Rightarrow c>b$

Rules for solving inequality equations:

These things do not affect the direction of the inequality:

• Add (or subtract) a number from both sides
• Multiply (or divide) both sides by a positive number
• Simplify a side

But these things do change the direction of the inequality (" $<$ " becomes " $>$ " for example):

• Multiply (or divide) both sides by a negative number
• Swapping left and right hand sides
• If there is a parenthesis $\left(\right)$ on the interval, then we use the strict inequality symbols $<\text{ or}>$

If there is a bracket $\left[\right]$ on the interval, then we use the inequality symbols

Calculation:

  $\begin{array}{l}4.5b\ge -12;b=-4\\ \frac{4.5b}{4.5}\ge \frac{-12}{4.5}\text{[}\text{Divide}\text{both}\text{sides}\text{by}4.5\text{]}\\ b\ge -2.7\end{array}$

Solution $b\ge -2.7$ means the number greater than or equal to 2.7.

As $b=-4$ is less than − 2.7, so the solution $b=-4$ is not true.

  

Thus, it means $b=-4$ is not true. False