We can use substitution to determine which value of \(\displaystyle x\) makes the inequality true. 

\(\displaystyle 5+4(8)=37\)

\(\displaystyle 34< 37\textup { TRUE}\)

\(\displaystyle 5+4(7)=33\)

\(\displaystyle 34< 33\textup{ FALSE}\), because \(\displaystyle 34>33\)

\(\displaystyle 5+4(6)=29\)

\(\displaystyle 34< 29\textup { FALSE}\), because \(\displaystyle 34>29\)

\(\displaystyle 5+4(5)=25\)

\(\displaystyle 34< 25\textup { FALSE}\), because \(\displaystyle 34>25\)

Because we are looking for a value of \(\displaystyle x\) that makes the expression greater than \(\displaystyle 34\), \(\displaystyle 8\) is our correct answer. 

We can use substitution to determine the value of \(\displaystyle x\). 

\(\displaystyle {\color{Teal} 12+7=19}\)

\(\displaystyle 12+8=20\)

\(\displaystyle 12+9=21\)

\(\displaystyle 12+10=22\)

\(\displaystyle 12+11=23\)

Because we are looking for the number that when added to \(\displaystyle 12\) equals \(\displaystyle 19\), our correct answer is \(\displaystyle 7\)

The amount of change given after a purchase is the amount the customer pays minus the cost of the item.  So the cost of the item is the amount the customer pays minus the amount of change received.

The measure of \(\displaystyle \angle2\) is twenty degrees greater than the measure \(\displaystyle x\) of \(\displaystyle \angle 1\), so its measure is 20 added to that of \(\displaystyle \angle 1\) - that is, \(\displaystyle x + 2 0\).

The measure of \(\displaystyle \angle 3\) is thirty degrees less than twice that of \(\displaystyle \angle 1\). Twice the measure of \(\displaystyle \angle 1\) is \(\displaystyle 2x\), and thirty degrees less than this is 30 subtracted from \(\displaystyle 2x\) - that is, \(\displaystyle 2x-30\).

The sum of the measures of the three angles of a triangle is 180, so, to solve for \(\displaystyle x\) - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

\(\displaystyle x + (x+20) + (2x-30) = 180\)

The measure of \(\displaystyle \angle2\) is forty degrees less than the measure \(\displaystyle x\) of \(\displaystyle \angle 1\), so its measure is 40 subtracted from that of \(\displaystyle \angle 1\) - that is, \(\displaystyle x -40\).

The measure of \(\displaystyle \angle 3\) is ten degrees less than twice that of \(\displaystyle \angle 1\). Twice the measure of \(\displaystyle \angle 1\) is \(\displaystyle 2x\), and ten degrees less than this is 10 subtracted from \(\displaystyle 2x\) - that is, \(\displaystyle 2x-10\).

The sum of the measures of the three angles of a triangle is 180, so, to solve for \(\displaystyle x\) - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

\(\displaystyle x + (x-40) + (2x - 10) = 180\)

Since there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans , then the number of pounds of Hazelnut Happiness beans is fourteen subtracted from \(\displaystyle x\):

\(\displaystyle x -14\).

Add the number of pounds of Pecan Delight beans, \(\displaystyle x\), to the number of pounds of Hazelnut Happiness beans, \(\displaystyle x -14\), to get the number of pounds of the mixture, which is \(\displaystyle 60\).

This translates to the following equation:

\(\displaystyle x + (x - 14) = 60\)

Since there are twelve more pounds of Vanilla Dream beans in the mixture than Strawberry Heaven beans, then the number of pounds of Vanilla Dream beans is twelve added to \(\displaystyle x\):

 \(\displaystyle x + 12\).

Add the number of pounds of Strawberry Heaven beans, \(\displaystyle x\), to the number of pounds of Vanilla Dream beans, \(\displaystyle x + 12\), to get the number of pounds of the mixture, which is \(\displaystyle 40\).

This translates to the following equation:

\(\displaystyle x + (x + 12) = 40\)

Our number sentence has the phrase "greater than" which means we have an inequality. 

"\(\displaystyle 93\) is greater than" can be written as \(\displaystyle 93>\) because we replace the words "greater than" with the greater than symbol. 

Next, we have "\(\displaystyle x\) minus \(\displaystyle 45\)". This can be written as \(\displaystyle x-45\) because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \(\displaystyle 93>x-45\)

Our number sentence has the phrase "greater than" which means we have an inequality. 

"\(\displaystyle 14\) is greater than" can be written as \(\displaystyle 14>\) because we replace the words "greater than" with the greater than symbol. 

Next, we have "\(\displaystyle x\) minus \(\displaystyle 19\)". This can be written as \(\displaystyle x-19\) because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \(\displaystyle 14>x-19\)

Our number sentence has the phrase "greater than" which means we have an inequality. 

"\(\displaystyle 72\) is greater than" can be written as \(\displaystyle 72>\) because we replace the words "greater than" with the greater than symbol. 

Next, we have "\(\displaystyle x\) minus \(\displaystyle 31\)". This can be written as \(\displaystyle x-31\) because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \(\displaystyle 72>x-31\)