Let a number be \(\displaystyle x\).  Split up the problem into parts.

A number less than three:  \(\displaystyle 3-x\)

Is less than three:  \(\displaystyle < 3\)

Combine all the terms.

The answer is:  \(\displaystyle 3-x< 3\)

Split up the sentence into parts.  Let the number be \(\displaystyle y\).

Two more than three times a number:  \(\displaystyle 3y+2\)

More than six:  \(\displaystyle >6\)

Combine the parts to form an inequality.

The answer is:  \(\displaystyle 3y+2>6\)

Break up the terms and rewrite by parts.

A number less than three:  \(\displaystyle 3-x\)

Greater than five:  \(\displaystyle >5\)

Combine the terms.

The answer is:  \(\displaystyle 3-x>5\)

Break up the statement into parts.  Let \(\displaystyle x\) be the number.

Three times a number:  \(\displaystyle 3x\)

Two less than three times a number:  \(\displaystyle 3x-2\)

Less than four:  \(\displaystyle < 4\)

Combine the terms.

The answer is:  \(\displaystyle 3x-2< 4\)

Break up the inequality into parts.  Let a variable be the number.

Twice a number:  \(\displaystyle 2x\)

Twice a number less than six:  \(\displaystyle 6-2x\)

Is more than four:  \(\displaystyle >4\)

Combine the terms.

The answer is:  \(\displaystyle 6-2x>4\)

In order to write this inequality, we need to break up the statement into parts.

Let the number be a random variable.

The difference of five and twice a number:  \(\displaystyle 5-2x\)

Twice the difference of five and twice a number:  \(\displaystyle 2(5-2x)\)

One less than twice the difference of five and twice a number:  \(\displaystyle 2(5-2x)-1\)

Is less than four:  \(\displaystyle < 4\)

Combine the terms.

The answer is:  \(\displaystyle 2(5-2x)-1< 4\)

Convert each part of the sentence into mathematical expressions.  Let a random variable be the number.

Five times a number:  \(\displaystyle 5x\)

Five times a number less than five:  \(\displaystyle 5-5x\)

Is less than negative five:  \(\displaystyle < -5\)

Combine the expressions.

The answer is:  \(\displaystyle 5-5x< -5\)

Let a number be \(\displaystyle x\).  Break up the sentence to parts.

Eight times a number:  \(\displaystyle 8x\)

Two less than eight times a number: \(\displaystyle 8x-2\)

Is at least seven:  \(\displaystyle \geq7\)

Combine the terms.

The answer is:  \(\displaystyle 8x-2\geq7\)

Split the problem statement into parts.

Two times a number:  \(\displaystyle 2x\)

Eight more than two times a number:  \(\displaystyle 2x+8\)

Is more than two:  \(\displaystyle >2\)

Combine the terms to make an equation.

The answer is:  \(\displaystyle 2x+8>2\)

Split the statement into parts.

Seven more than a number: \(\displaystyle x+7\)

Is less than five:  \(\displaystyle < 5\)

Combine both parts to form an inequality.

The answer is:  \(\displaystyle x+7< 5\)