The first step is to distribute (multiply) through the parentheses:

Then subtract from both sides of the inequality:

Next, subtract the 12:

Finally, divide by two:

Write the following as a mathematical inequality:

A number is less than or equal to three times the sum of another number and five.

Let's begin with

"A number" let's call it x

"...is less than or equal to..."

So far we have:

Now,

"...three times..."

"...the sum of another number and five."

So, all together:

To solve , it is necessary to isolate the variable and the integers.

Subtract and from both sides of the equation.

Divide by nine on both sides.

This answer is also the same as:

Seven less than two times a number is greater than fourteen.

Let's look at the problem step by step.

If we do not know the value of a number, we give it a variable name. Let's say x. So, we see in the problem

Seven less than two times a number is greater than fourteen.

So, we will replace a number with x.

Seven less than two times x is greater than fourteen.

Now, we see that is says "two times" x, so we will write it like

Seven less than 2 x is greater than fourteen.

The problem says "seven less" than 2x. This simply means we are taking 2x and subtracting seven. So we get

2x - 7 is greater than fourteen

We know the symbol for "is greater than". We can write

2x - 7 > fourteen

Finally, we write out the number fourteen.

2x - 7 > 14

Split the problem statement into parts.

Two times a number:

Eight more than two times a number:

Is more than two:

Combine the terms to make an equation.

The answer is:

Split the sentence into parts.

A number cubed:

Four more than a number cubed:

Is less than five:

Combine the terms to form the inequality.

The answer is:

To solve, you must convert the statement into an expression. The key work is "is". Whatever is on the left of that in the sentence will be on the left side of the expression. The same goes for the right. Thus, is on the left and is on the right.

Break up the sentence into parts.

Twice a number:

Nine more than twice a number:

Is at least fifteen:

Combine the terms to form an inequality.

The answer is:

We begin by using inverse operations, exactly as if we were solving an equation. In this case, we must isolate the variable by subtracting from both sides. This leaves us with . Finally, we again use inverse operations--in this case dividing by --to end up with a final inequality of . Note that we do not flip the inequality because we are not dividing by a negative number.

Break up the terms and rewrite by parts.

A number less than three:

Greater than five:

Combine the terms.

The answer is: