Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1081 : Linear Equations

Write the equation:  Fourteen more than thrice a number is fifteen.

Possible Answers:

Correct answer:

Explanation:

Split up the sentence into parts.

Thrice a number:  

Fourteen more than thrice a number:  

Is fifteen:  

Combine the terms to form an equation.

The answer is:  

Example Question #166 : How To Write Expressions And Equations

Write the equation:  Four times the quantity of four times a number is equal to six.

Possible Answers:

Correct answer:

Explanation:

Break up the statement into parts.

Four times a number:  

Four times the quantity of four times a number:  

Is equal to six:  

The answer is:  

Example Question #161 : How To Write Expressions And Equations

Write the equation:  Twelve more than six times the square of a number is negative four.

Possible Answers:

Correct answer:

Explanation:

Break up the question in parts.

The square of a number:  

Six times the square of a number:   

Twelve more than six times the square of a number:  

Is negative four:  

Combine the terms to form an equation.

The answer is:  

Example Question #1083 : Linear Equations

Write the equation:  Five less than six times a number is twelve.

Possible Answers:

Correct answer:

Explanation:

Break up the sentence into parts.

Six times a number:  

Five less than six times a number:   

Is twelve:  

Combine the parts to form an equation.

The answer is:  

Example Question #1081 : Algebra 1

Write the expression:  Six less than twice a number.

Possible Answers:

Correct answer:

Explanation:

To write the expression, split the sentence into parts.  An expression does not have an inequality or equal sign.

Twice a number:  

Six less than twice a number:  

The answer is:  

Example Question #2 : Complex Numbers

Divide:

Answer must be in standard form.

Possible Answers:

Correct answer:

Explanation:

Multiply both the numerator and the denominator by the conjugate of the denominator which is  resulting in

This is equal to 

Since  you can make that substitution of  in place of  in both numerator and denominator, leaving:

 

When you then cancel the negatives in both numerator and denominator (remember that , simplifying each term), you're left with a denominator of  and a numerator of , which equals .

Example Question #1 : Percents

45 is what percent of 75?

Possible Answers:

Correct answer:

Explanation:

Let equal the decimal value of our answer. We can set up the following equation.

 (i.e. 75 times what percent equals 45?)

Divide both sides by 75.

Multiply by 100 to get the percentage value of the decimal.

%

Example Question #1 : Percents

In a bag of marbles, Barry has 20 green ones and 40 red ones.  If he adds 7 green and 9 red, what percentage (to the nearest hundreth) of the marbles will be green?

Possible Answers:

0.36%

33.33%

35.52%

0.33%

35.53%

Correct answer:

35.53%

Explanation:

First, you need to add in the marbles.  This will give you 27 green and 49 red.  The total number of marbles in the bag are 76.  To find the percentage of green marbles, all you need to do is divide 27 by 76, which gives you 0.35526315789474 or 35.526315789474%.  Rounding to the nearest percent, you get 35.53%.

Example Question #2 : Percents

Let  be a positive real number. In terms of , what percent of  is 20?

Possible Answers:

 %

 %

 %

 %

 %

Correct answer:

 %

Explanation:

Set up a proportion statement.

Solve for :

Example Question #1 : Percents

Let  be a positive real number. In terms of , what percent of 25 is ?

Possible Answers:

 %

 %

 %

 %

 %

Correct answer:

 %

Explanation:

Set up a proportion statement.

Solve for :

Learning Tools by Varsity Tutors