Chapter 5, Problem 13MCQ

To determine

To solve the inequality:

  $2m\le -10$

And check the solution.

Answer to Problem 13MCQ

  $\left(-\infty ,15\right]$

Explanation of Solution

Given:

  $2m\le -10$

Concept Used:.

• To check the answer solution for the given inequality

1. First check the solution at end point by converting it into an equation.
2. If the solution is $x<m$, then pick any value of x less than m and check whether it satisfies the inequality.
3. If the solution is $x>m$, then pick any value of x greater than m and check whether it satisfies the inequality.

Properties of inequality:

1. $b\le c\Rightarrow ab\le ac,\text{ if }a\ge 0$
2. $b\le c\Rightarrow ab\ge ac,\text{ if }a\le 0$

Calculation:

To solve the inequality:

  $2m\le -10$

Divide both sides of the inequality with $2$ , as

  $\begin{array}{l}2m\le -10\\ \Rightarrow \frac{2m}{2}\le \frac{-10}{2}\\ \Rightarrow m\le -5\end{array}$

Thus, the inequality is true for m less than or equal to $-5$ , thus the solution of given inequality in interval form is:

  $\left(-\infty ,-5\right]$

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting m equals to $-5$ in left hand side

  $\begin{array}{c}2\left(-5\right)=-10\\ =\text{Right Hand}\end{array}$

Now put any value any value of m less than $-5$ , say $-9$ and check whether it satisfies the inequality, as

  $\begin{array}{l}2\left(-9\right)=-18\\ \text{And }-18<-10\end{array}$

Since, both conditions are satisfied thus solution of inequality is correct.