Chapter 2.6, Problem 33E

To determine

To explain:whether the given statement is true or false

Answer to Problem 33E

The given statement is false

Explanation of Solution

Given:

If a is the solution of $|x+3|\ge 8$ then a is also solution of $x+3>-8,$ .

Calculation:

In solving absolute value inequalities, remember that $|ax+b|<c$ provided that $c>0$ will either be:

  $ax+b>-c\text{ AND }ax+b<c$

Also, $|ax+b|>c$ provided that $c>0$ will either be:

  $ax+b<-c\text{ OR }ax+b>c$

In graphing the inequalities, remember that inequalities joined by "and" is the intersection of the inequalities while those joined by "or" is the union of the inequalities.

Since writing $|x+3|\ge 8$ into a compound inequality brings out $x+3\le$ -8 OR $x+3\ge 8,$ then this statement is FALSE.

Conclusion:

The given statement is false