Question

Write an inequality that compares the given numbers. Does the inequality remain true when you multiply each number in the inequality by $2$? By $-2$? Justify your answers.

$-2;5$

Answer 1

Step : Write the inequality

We have two numbers $-2and5$.

So, an inequality relation that relates these numbers is $-2<5$.

Step 2 : Multiply each numbers by $2$

New inequality relation is

$$\begin{gathered} \Rightarrow -2\times 2<5\times 2 \\ \therefore -4<10 \end{gathered}$$

So, the inequality relation remains the same when we multiply both numbers by a positive number.

Step 3 : Multiply each numbers by $-2$

New inequality relation is

$$\begin{gathered} \Rightarrow -2<5 \\ \Rightarrow -2\times \left(-2\right)>5\times \left(-2\right) \\ \therefore 4>-10 \end{gathered}$$

So, the inequality relation gets reversed the same when we multiply both numbers by a negative number.