Chapter 5, Problem 10MCQ

To determine

To solve the inequality:

  $\frac{1}{3}y\le 5$

And check the solution.

Answer to Problem 10MCQ

  $\left(-\infty ,15\right]$

Explanation of Solution

Given:

  $\frac{1}{3}y\le 5$

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:

  $\frac{1}{3}y\le 5$

Multiply both sides of the inequality by 3, as

  $\begin{array}{l}\frac{1}{3}y\le 5\\ \Rightarrow 3\times \frac{1}{3}y\le 3\times 5\\ \Rightarrow y\le 15\end{array}$

Thus, the inequality is true for y less than $15$ , thus the solution of given inequality in interval form is:

  $\left(-\infty ,15\right]$

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting y equals to $15$ in left hand side

  $\begin{array}{c}\frac{15}{3}=5\\ =\text{Right Hand}\end{array}$

Now put any value any value of y less than $15$ , say $12$ and check whether it satisfies the inequality, as

  $\frac{12}{3}=4<5$

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