"The product of seven and a number " is \(\displaystyle 7x\). "Twenty subtracted from the product of seven and a number" is \(\displaystyle 7x - 20\) . "Exceeds one hundred" means that this is greater than one hundred, so the correct inequality is

\(\displaystyle 7x - 20 > 100\)

"The sum of a number and sixteen" is translates to \(\displaystyle x + 16\); twice that sum is \(\displaystyle 2(x+16)\). " Is no less than sixty" means that this is greater than or equal to sixty, so the desired inequality is

 \(\displaystyle 2(x+16) \geq 60\).

"The sum of a number and sixteen" translates to \(\displaystyle x + 16\); twice that sum is \(\displaystyle 2 (x+16)\). "Does not exceed eighty" means that it is less than or equal to eighty, so the desired inequality is

\(\displaystyle 2 (x+16) \leq 80\)

The way the sentence is phrased suggests that the person can spend up to \(\displaystyle 20\) dollars but not a penny more. This suggests that \(\displaystyle s\), the amount spend can be \(\displaystyle 20\) but not exceed it. 

So your answer is: \(\displaystyle s\leq20\)

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, \(\displaystyle a\) is on the left and \(\displaystyle 2b\) is on the right.

\(\displaystyle a>2b\)

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:

\(\displaystyle x\leq\)

Now,

"...three times..."

\(\displaystyle 3*\)

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

\(\displaystyle 3(y+5)\)

So, all together:

\(\displaystyle x\leq3(y+5)\)

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

Twice a number:  \(\displaystyle 2x\)

Two less than twice a number:  \(\displaystyle 2x-2\)

Less than two:  \(\displaystyle < 2\)

Combine the parts.

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

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

Twice a number:  \(\displaystyle 2x\)

Three less than twice a number:  \(\displaystyle 2x-3\)

Three less than twice a number is more than:  \(\displaystyle 2x-3>\)

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

Combine the terms to form the inequality.

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

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:  \(\displaystyle 3-x< 3\)