# Algebra 1 : How to write expressions and equations

## Example Questions

### Example Question #101 : How To Write Expressions And Equations

Translate the following sentence into a mathematical expression:

Eight less than three times a number is equal to four more than two times that same number.

Explanation:

Let's start with the first half of the sentence, "eight less than three times a number". We can translate the written English into mathematical terms in the order that we read them. "Less than" means that we are going to be subtracting something (in this case ) from another value. That other value is "three times a number", which means  multiplied by a number. We aren't told what this number is, but that doesn't matter, because we can just use  instead. Now let's put together that first half of the sentence in math terms:

The next part of the sentence, "is equal to", tells us that we need to insert an equal sign into the equation next:

Now let's look at the last part of the sentence, "four more than two times that same number". "More than" means that we are going to be adding something (in this case ) to another value. That other value is  "two times that same number", which lets us know that multiplcation is now involved. We are going to use that same number we used in the first half the sentence, we chose , and we're going to multiply that number by . Now let's put together the complete second half of the sentence in math terms:

And we can now place this on the other side of the equal sign to get a complete mathematical expression:

### Example Question #102 : How To Write Expressions And Equations

Greg, an avid fan of horticulture, decides to buy a tree for his backyard. After spending 20 minutes browsing his local nursery, Greg settles for a young pine tree which is initially 1.5 feet tall and costs 15 dollars. Greg then plants the tree in his backyard and decides to measure its growth over time. His measurements show that after one day the tree is 1.7 feet tall and after two days the tree is 1.9 feet tall. Which of the following presents a linear model of the height, y, of Greg's tree as a function of the number of days, x, which have passed since the tree was planted?

Explanation:

Immediately, one must realize that two pieces of extraneous information are given, including the cost of the tree and the time spent browsing the store.

Then realize that the rate of growth of the tree is equal to the slope of the linear growth model.

This rate is given by

.

Also, one must realize that the initial height of the tree is 1.5 feet and represents the y intercept of the linear growth model.

Now, with this information, it is possible to simply use the slope intercept model of a line  to predict the equation of the linear growth model.

Substitute 0.2 for the slope term, m, and 1.5 for the y intercept term, b, to obtain the final linear growth model,

.

### Example Question #103 : How To Write Expressions And Equations

Express  more than .

Explanation:

Take every word and translate into math.  more than means that you need to add  to something. That something is  so just combine them to have an expression of

### Example Question #104 : How To Write Expressions And Equations

Express  less than .

Explanation:

Take every word and translate into math.  less than means that you need to subtract  to something. That something is  so just combine them to have an expression of

### Example Question #105 : How To Write Expressions And Equations

Express  less than .

Explanation:

Take every word and translate into math.  less than means that you need to subtract  to something. That something is  so just combine them to have an expression of

### Example Question #106 : How To Write Expressions And Equations

Express  times .

Explanation:

Take every word and translate into math. Times indicates multiplication. So we multiply  and  to get .

### Example Question #107 : How To Write Expressions And Equations

Express the quotient of  and .

Explanation:

Take every word and translate into math. Quotient indicates division. So we have  listed first being the numerator and  listed last being the denominator. Our answer is .

### Example Question #108 : How To Write Expressions And Equations

Express the sum of  times  and quotient of  and .

Explanation:

Take every word and translate into math. Sum means addition. Times indicates multiplication. So we multiply  and  to get . Quotient indicates division. So we have  listed first being the numerator and  listed last being the denominator. Overall, we have . Finally, putting it together, we get

### Example Question #109 : How To Write Expressions And Equations

Express the difference of  times  and quotient of  and .

Explanation:

Take every word and translate into math. Difference means subtraction. Times indicates multiplication. So we multiply  and  to get . Quotient indicates division. So we have  listed first being the numerator and  listed last being the denominator. Overall, we have . Finally, putting it together, we get

### Example Question #110 : How To Write Expressions And Equations

Express the quotient of  and