The product of a number and -8 decreased by 13 is less than or equal to 27

Answer 1

-8n-13≤27

8n+13≥-27

8n≥-40

n≥-5

Why did the inequality get reversed?

Suppose -a≥-b

Add a to each side

0≥-b+a

Add b to each side

b≥a i.e. a≤b

Answer 2

Hi, Mia.

Okay, so the product of a number and -8 is the number (let's call it n) times -8. So that product (-8n) decreased by 13 is less than or equal to 27

So you have:

-8n - 13 ≤ 27

Now, solve for n:

-8n -13+13 ≤ 27 + 13

-8n ≤ 40

Now, to divide both sides by a negative number (-8), you must change the inequality to ≥:

-8n/-8 ≥ 40/-8

n ≥ -5

Answer 3

Suppose x is the unknown number then

-8*x-13 <= 27 ADD 13 on both sides to isolate -8x on the left

-8x <= 40 DIVIDE both sides by -8; Note that it will switch the inequality sign

x >= -5 That is your answer!