Algebra 1 : How to write expressions and equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : How To Write Expressions And Equations

Write in simplest form:

Possible Answers:

Correct answer:

Explanation:

Rewrite, then distribute:

Example Question #2 : How To Write Expressions And Equations

A car travels at a speed of 60 miles per hour. It is driven for 2.5 hours. How many miles does it travel?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, you need to construct an algebraic equation. If  is the distance traveled, then  must equal to the speed multiplied by the time travelled. In this case, , which gives you a result of 150 miles. 

Example Question #3 : How To Write Expressions And Equations

Rewrite the expression in simplest terms, where  is the imaginary number .

Possible Answers:

Correct answer:

Explanation:

Writing this expression in simplest terms can be achieved by first factoring the radical into its smallest factors.

Multiplying the two  together results in . Multiplying this by  (which is simplified to ) results in the answer   .

Example Question #4 : How To Write Expressions And Equations

 

Rewrite the equation for  in terms of .

 

Possible Answers:

 

Correct answer:

Explanation:

The goal in expressing  in terms of  is to isolate  on one side of the equation. One way to do this is to factor  out of the fraction on the right side of the equation, then divide the entire equation by the fraction that remains after factoring. Remember that dividing by a fraction is the same as multiplying by the reciprocal of that fraction.

The left side of this equation will simply resolve into , although there are still  variables on the right, so this is not yet in terms of . The right side resolves based on the rules for multiplying and dividing variables with exponents (add the exponents of like variables being multiplied, subtract the smaller exponent from the larger in the case of division, and change the variable to a  if the resulting exponent is ).


 

Since there is still a  in the numerator on the right side of the equation, we will need to divide both sides of the equation by .

We have no solved for the reciprocal of  in terms of . We simply flip both sides of the equation to get our answer.

Example Question #5 : How To Write Expressions And Equations

Translate this sentence into a mathematical equation:

Three less than five times a number is the same as two more than twice that number.

Possible Answers:

Correct answer:

Explanation:

Three less than five times a number is the same as two more than twice that number.

Let the number be .

"Three less than five times a number" translates into .

"Is the same as" means equal to or "".

"Two more than twice that number" means .

Putting these together gives:

Example Question #6 : How To Write Expressions And Equations

For the given equation determine the slope:

Possible Answers:

Correct answer:

Explanation:

By changing the equation to slope intercept form we get the following:

 

 

Hence the slope is

Example Question #7 : How To Write Expressions And Equations

What is the slope and the  and  intercepts of a line which passes through  and ?

Possible Answers:

slope = 0, x-int = 2, y-int = -3

slope = 1, x-int = 2, y-int = 2

slope = undefined, x-int = -3, y-int = none

slope = 0, x-int = -3, y-int = 2

slope = undefined, x-int 2, y-int = -3

Correct answer:

slope = undefined, x-int = -3, y-int = none

Explanation:

For a vertical line e.g. and

This line does not intersect the  and hence there is no .

Since the line passes through  hence the -intercept .

Example Question #8 : How To Write Expressions And Equations

Write the equation of a line with a slope of

  

and passes through the point .

Possible Answers:

Correct answer:

Explanation:

Here we use the point-slope formula of a line which is

By plugging in , and  values we get the following:

which is equal to

When the above is simplified we get:

 

Example Question #9 : How To Write Expressions And Equations

Complete the missing information for the equation of the following line

and determine which one of the  coordinates is not a solution to the above equation.

Possible Answers:

Correct answer:

Explanation:

Replacing  with , one gets  which tells us that  is not a solution.

Example Question #10 : How To Write Expressions And Equations

Convert the following into the standard form of a line:

 

Possible Answers:

Correct answer:

Explanation:

Multiplying each term of the given equation by the denominator of the slope which is 5 one gets :

 

 

which can be written as


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