Question

Which inequality is equivalent to$-18\le 3p$?

1. $p\ge -54$
2. $-54\ge p$
3. $p\ge -6$
4. $-6\ge p$

Short answer

The correct option is (c) & (d).

Step-by-step solution

Step -1 - Apply the concept of linear equations

In this type of inequality, Simply use the property of addition or subtraction of suitable number on both Left Hand Side & Right Hand Sideto maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Step -2 – Find the value of p

Here, the inequality is $-18\le 3p$

To solve this, simply dividing $3$to both side of the equation

$\begin{array}{l}-18\le 3p\\ \frac{-18}{3}\le \frac{3p}{3}\\ -6\le p\\ p\ge -6\end{array}$

Step -3 – Eliminating the options to get correct one

a. $p\ge -54$:This is not a correct option because the solution of the inequality is $p\ge -6$.

b. $-54\ge p$: This is not a correct option because the solution of the inequality is $p\ge -6$.

c. $p\ge -6$: This is a correct option because the solution of the inequality is $p\ge -6$.

d. $-6\ge p$: This is also a correct option because the solution of the inequality is $p\ge -6$ or $-6\ge p$.