ISEE Lower Level Quantitative : How to find the solution to an equation

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

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Example Questions

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Example Question #1 : Algebraic Concepts

What is the value of x in the equation?

\dpi{100} \frac{200+50}{5}=x

Possible Answers:

\dpi{100} 5

\dpi{100} 100

\dpi{100} 50

\dpi{100} 25

Correct answer:

\dpi{100} 50

Explanation:

First, add \dpi{100} 200+50=250.

Next, divide \dpi{100} 250\div 5=50.

So \dpi{100} x=50

Example Question #2 : Algebraic Concepts

Simplify.

Possible Answers:

Correct answer:

Explanation:

When simplifying an expression, you must combine like terms. There are two types of terms in this expression: “x’s” and whole numbers.  Combine in two steps:

1) x’s:  

2) whole numbers:   

The simplified expression is: .

Example Question #3 : Algebraic Concepts

Solve, when .

Possible Answers:

Correct answer:

Explanation:

To solve, insert  for each :

Simplify:

 

*Common error: When solving this part of the equation  always remember the order of operations (PEMDAS) and square the number in the () BEFORE multiplying!

Example Question #4 : Algebraic Concepts

Solve for .

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Algebraic Concepts

Use the equations to answer the question. 

What is ?

Possible Answers:

Correct answer:

Explanation:

First, you need to find what would make  and  true in their respective equations.  equals 1 and  equals 4. The next step is to add those together, which gives you 5. 

Example Question #6 : How To Find The Solution To An Equation

What story best fits the expression ?

Possible Answers:

Jonah had 3 baseball cards, but after his friend gave him some, he had 12. 

Michelle had 3 stuffed animals and gave 1 away.

Nell bought 9 bags of candy with 3 pieces of candy in each bag. 

Lisa had 9 pencils with two erasers each.

Correct answer:

Nell bought 9 bags of candy with 3 pieces of candy in each bag. 

Explanation:

Nell's story fits best because if she bought 9 bags with 3 pieces each, that would be 27 total. This fits best with the  equation.

Example Question #6 : Algebraic Concepts

What is  equal to in this equation: 

Possible Answers:

Correct answer:

Explanation:

Find the number that makes the equation true. 2 works because when plugged in, the left side of the equation becomes 13, making the whole equation true.

Example Question #7 : Algebraic Concepts

Five more than a number is equal to  of twenty-five . What is the number?

Possible Answers:

Correct answer:

Explanation:

From the question, we know that  plus a number equals  of . In order to find out what  of  is, multiply  by .  

 

, or .

The number we are looking for needs to be five less than , or .

You can also solve this algebraically by setting up this equation and solving:

 

Subtract  from both sides of the equation.         

 

Example Question #8 : Algebraic Concepts

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , we want to isolate , or get it by itself. 

Add to both sides of the equation.

            

Now we need to divide both sides by the coefficient of , i.e. the number directly in front of the .

     

Example Question #10 : How To Find The Solution To An Equation

Solve for .

Possible Answers:

Correct answer:

Explanation:

First, subtract the three from both sides:

Then, divide by three on both sides:

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