Choose the correct mathematical expression of the sentence,"A number  is less than or equal to seventeen."

This sentence contains the phrase "less than or equal to." This means that we need to write an inequality. When writing inequalities, always remeber that the pointed end points to the smaller of the two values.

So, we have "A number  ..."

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

See how the inequality sign has the pointy end facing the ? The pointy end should always face the smaller of the two values, and the open end should always face the larger of the two values. I was always taught that the inequality sign is like a hungry alligator. It always wants to eat the larger number!

Anyway,"...seventeen"

So we have our inequality. Note the horizontal line in the inequality sign. That is where we get the "...or equal to..." part.

The way the sentence is phrased suggests that the person can spend up to  dollars but not a penny more. This suggests that , the amount spend can be  but not exceed it. 

So your answer is: 

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 2x 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

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.

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:

In order to write the inequality, we must find the key words in the sentence.  

Write the equations from the following key words.  Let  be the height.

More than 40 inches tall:  

No greater than 70 inches:  

No greater than a certain height means it can be at that height, but cannot be greater than the given height.

The inequalities can be combined to a compound inequality:

The answer is:  

When writing statments as inequalities, you must take it one step at a time.  So in the statement

Two times the sum of  and  is greater than half of the product of  and .

we will rewrite it one part at a time.

Two times the sum of  and  is greater than half of the product of  and .

 times the sum of  and  is greater than half of the product of  and .

 the sum of  and  is greater than half of the product of  and .

 is greater than half of the product of  and .

 half of the product of  and .

  of the product of  and .

Simplify.

Break up the statement by parts.  Let that number be .

Twice a number:  

Two less than twice a number:  

Less than two:  

Combine the parts.

The answer is:  

Break up the sentence into parts.  Let the number be .

Twice a number:  

Three less than twice a number:  

Three less than twice a number is more than:  

Three times the number:  

Combine the terms to form the inequality.

The answer is:  

Let a number be .  Split up the problem into parts.

A number less than three:  

Is less than three:  

Combine all the terms.

The answer is: