Question

Suppose A< - 1 what must be true about the value of b so that ab< a

Answer 1

b must be positive

Explanation:

if a is less than -1

that means to get smaller numbers

b needs to be positive

so that when a is multiplied by b you would have

numbers that are more negative

Answer 2

b > 1

Explanation:

Given:

• a < -1
• ab < a

Substituting a = -1 into ab < a

⇒ (-1)b < -1

⇒ -b < -1

⇒ b > 1

If a < -1 then a is negative. If ab < a then ab is also negative.

In order for ab to be negative (when a is negative) b must be positive.

For ab < a then b > 1.

Proof

If b = 0.5 and a = -1.5 then ab = -0.75

As -0.75 > -1.5 then ab > a so this cannot be true.

If b = 1.5 and a = -1.5 then ab = -2.25

As -2.25 < -1.5 then ab < a so this is true.

Therefore b > 1