Question

Given the inequality -8 < 2, explain what happens when you multiply or divide both sides by 2 and what happens when you multiply or divide both sides by -2.

Answer 1

Dividing both sides by 2= -8÷2 < 2÷2 = -4 < 1

multiplying both sides by 2= -8×2 < 2×2 = -16<4

dividing both sides by -2= -8÷ -2 < 2÷ -2 = 4> -1

multiplying both sides by -2= -8× -2 < 2× -2= 16> -4

Answer 2

Concept:

We need to understand how division and multiplications work in inequalities.

When negative is multiplied or divided by inequality, then the inequality changes.

Given:

We are given an inequality -8<2.

To find:

We need to find what happens when you multiply or divide both sides by 2 and -2.

Solution:

Let's begin with multiplying by 2

-8×2 < 2×2

⇒-16 < 4

then we divide by 2

$-\frac{8}{2} < \frac{2}{2}$

⇒-4 < 1

Now, we can start by multiplying with -2

(-8)×-(2) < 2×(-2)

⇒16 > -4                 [When negative is multiplied or divided by inequality,                         .                                then the inequality changes.]

Next, we divide by -2

$\frac{-8}{-2} < \frac{2}{-2}$

⇒4 > -1

Therefore,

1. By multiplying by 2 we get 16 < 4

2. By dividing by 2 we get -4 < 1

3. By multiplying by -2 we get 16 > -4

4. By dividing by -2 we get 4 > -1