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. $4;-1$

Answer 1

Step 1 : Write the inequality

We have two numbers, $4and-1$.

An inequality relation between these two numbers is $4>-1$.

Step 2 : Multiply by $2$

New inequality relation is

$$\begin{gathered} \Rightarrow 4\times 2>\left(-1\right)\times 2 \\ \therefore 8>-2 \end{gathered}$$

Hence, the inequality relation remains same by multiplying with a positive number.

Step 3 : Multiply by $-2$

New inequality relation is

$$\begin{gathered} \Rightarrow 4\times \left(-2\right)>\left(-1\right)\times \left(-2\right) \\ \therefore -8<2 \end{gathered}$$

Hence, the inequality relation gets reversed by multiplying with a negative number.