Question

How do We solve compound inequalities $5x + 5 > 15$ ?

Answer 1

Hint: For solving the given inequality $5x + 5 > 15$, we have to solve for $x$ . We just need to remember to apply all of our operations to both the parts, like adding , subtracting , multiplying, and dividing .

Complete step-by-step solution:
The given inequality is $5x + 5 > 15$.
We just need to remember to apply all of our operations to both the parts.
Subtract $5$ from both the side of the inequality ,
$
   \Rightarrow 5x + 5 - 5 > 15 - 5 \\
   \Rightarrow 5x > 10 \\
 $
Divide both the side of the inequality by $5$,
$ \Rightarrow \dfrac{{5x}}{5} > \dfrac{{10}}{5}$
$ \Rightarrow x > 2$
Therefore $x \in (2,\infty )$ .

Additional Informational: Inequalities are often manipulated like equations and follow terribly similar rules, however there's one necessary exception. If We add constant variety to each side of given inequality , the inequality remains true. If We subtract constant variety from each side of the given inequality , the inequality remains true. If We multiply or divide each side of the given inequality by constant positive variety, the inequality remains true. However, if We 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 tend to multiply each side of this inequality by a negative number, we've got to reverse the inequality , giving $ - 4 < - 2$ in order for it to be true.

Note:Point to be remembered for inequality:
-We can add constant amount to every aspect
-We can subtract constant amount from both sides
-We can multiply or divide both sides by a constant positive amount .
-If We multiply or divide both sides by a negative amount, the inequality needs to be reversed.