ISEE Lower Level Quantitative : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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Example Questions

Example Question #31 : Algebraic Concepts

Which equation first the description?

Half of the difference of  and a number is .

Possible Answers:

Correct answer:

Explanation:

In order to choose the right answer, you must know which mathematical operations each of these words refer to:

"Half of": Divide by two

"Difference": Subtract a number

"A number" or "An unknown number": The unknown number is a variable; let's call it 

"is" or "is equal to": add an equal sign

 

So, in the problem "Half of the difference of  and a number is ," we are looking for half of "the difference of 20 and a number". That is written as:

If that is equal to , the answer is:

Example Question #31 : How To Find The Solution To An Equation

Which equation fits the description?

The sum of two different numbers and  is .

Possible Answers:

Correct answer:

Explanation:

In order to choose the right answer, you must know which mathematical operations each of these words refer to:

"Sum": Add numbers

"A number" or  "An unknown number": The unknown number is a variable; let's call it 

"Is" or "is equal to": add an equals sign

So, in the problem "The sum of two different numbers and  is ," we are looking to add two different variables to  that will equal .

The answer cannot be  because the problem asks for two different variables.  represents two of the same number.

The answer is 

Example Question #32 : How To Find The Solution To An Equation

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve an equation, first combine like terms. Move the  over to the other side of the equation by adding .

   

            

       

Next, remove the  from the variable by dividing by .

The answer is .

Example Question #33 : How To Find The Solution To An Equation

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve an equation, first combine like terms. Move the  over to the other side of the equation by adding .

   

          

             

Next, remove the  from the variable by dividing by .

The answer is .

Example Question #34 : How To Find The Solution To An Equation

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve an equation, first combine like terms. Move the  over to the other side of the equation by adding .

   

          

           

Next, remove the  from the variable by dividing by .

The answer is .

Example Question #32 : Algebraic Concepts

The sum of  and 6 is 56. What is the number?

Possible Answers:

Correct answer:

Explanation:

"The sum of  and  is " can be represented by the equation:

To solve an equation, first combine like terms. Move the  to the other side of the equation by adding 

     

        

The answer is .

Example Question #36 : How To Find The Solution To An Equation

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve an equation, first combine like terms. Move the  over to the other side of the equation by adding .

   

            

        

Next, remove the  from the variable by dividing by .

The answer is .

Example Question #33 : Algebraic Concepts

What is the value of  in the equation ?

Possible Answers:

Correct answer:

Explanation:

To solve for , you must get it alone on one side.

Start by subtracting both sides by .

Multiply both sides by .

Example Question #34 : Algebraic Concepts

What is the value of  in the equation ?

Possible Answers:

Correct answer:

Explanation:

Start by subtracting  from both sides.

Multiply both sides by .

Example Question #35 : Algebraic Concepts

What is the value of  in the equation ?

Possible Answers:

Correct answer:

Explanation:

To solve for , you will need to get it alone on one side.

Start by adding  to both sides.

Divide both sides by .

 

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