One third of the opposite of a number is less than 12

The number would be greater then 36.

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

Let x represent the unknown number.  The opposite of this number would be represented by -x.

1/3 of this is found by multiplying by 1/3; this gives us

1/3×(-x)

Since it is less than 12, this gives us

1/3×(-x) < 12

To cancel the 1/3, we can multiply both sides by 3:

1/3×(-x)×(3) < 12×(3)

-x < 36

We can cancel the negative by dividing both sides by -1.  When we multiply or divide an inequality by a negative number we flip the inequality:

-x/-1 < 36/-1

x > 36

Our number must be greater than 36.

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Answer:

The number would be greater then 36.

Step-by-step explanation:

Let x represent the unknown number.  The opposite of this number would be represented by -x.

1/3 of this is found by multiplying by 1/3; this gives us

1/3(-x)

Since it is less than 12, this gives us

1/3(-x) < 12

To cancel the 1/3, we can multiply both sides by 3:

1/3(-x)(3) < 12(3)

-x < 36

We can cancel the negative by dividing both sides by -1.  When we multiply or divide an inequality by a negative number we flip the inequality:

-x/-1 < 36/-1

x > 36

Our number must be greater than 36.