What is a number increased by three is greater than zero or less than or equal to negative three?

Question

I am lost

Answer 1

Let's begin by deciphering what each word means into math terms:

1. What is a number can be represented as the variable "x"
2. Increased by three means we are adding 3 to the variable "x" so we then will have: "x+3"
3. Is greater than zero can be translated to " > 0". If we put step 2 together with this step, we have: "x+3 > 0"
4. Or less than or equal to negative three can be translated to "<= -3". If we put step 2 together with this step, we have: "x+3 <= -3"

Now we have two inequalities we can solve for:

1. x+3 > 0
2. x+3 <= -3

Solving for inequality 1 gives us:

x+3 > 0

-3 -3

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x > -3

Solving for inequality 2 gives us:

x+3 <= -3

-3 -3

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x <= -6

From the inequalities we found, the variable x can be any number that is in the interval (-infinity, -6] U (-3, infinity).