Question

How do you solve compound inequalities $ - 10 < - 2 + 8x < 22$ ?

Answer 1

Hint:For solving this compound inequality $ - 10 < - 2 + 8x < 22$ , . We just need to remember to apply all of our operations to all three parts, like adding , subtracting , multiplying and others .

Complete solution step by step:
We just need to remember to apply all of our operations to all
three parts, like adding $2$:
\[
\Rightarrow - 10 + 2 < - 2 + 8x + 2 < 22 + 2 \\
\Rightarrow - 8 < 8x < 24 \\
\]
Now divide all the three parts by $8$
$
\Rightarrow \dfrac{{ - 8}}{8} < \dfrac{{8x}}{8} < \dfrac{{24}}{8} \\
\Rightarrow - 1 < x < 3 \\
$
Therefore $x \in ( - 1,3)$ .
Additional Informational:
Inequalities are often manipulated like equations and follow terribly similar rules, however there#39;s one necessary exception. If you add constant variety to each side of given inequality , the inequality remains true. If you subtract constant variety from each side of the given inequality , the inequality remains true. If you multiply or divide each side of the given
inequality by constant positive variety, the inequality remains true. However, if you multiply or divide each side of the given inequality by a negative variety, the inequality isn't any longer true. In fact, the inequality becomes reversed. This can be quite simple to visualize as a result of we will write that $4 > 2$ . However, if we have a tendency to multiply each side of this inequality , we have we've got to reverse the inequality , giving $ - 4 < - 2$ in order for it to be true.

Note: In inequality:
•you can add constant amount to every aspect
•you can subtract constant amount from both sides
•you can multiply or divide both sides by a constant positive amount .
If you multiply or divide both sides by a negative amount, the inequality needs to be reversed.