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ISEE Lower Level Quantitative : Algebraic Concepts

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

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #1 :How To Find The Solution To An Equation

What is the value of x in the equation?

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

Possible Answers:

$\dpi{100} 25$

$\dpi{100} 5$

$\dpi{100} 100$

$\dpi{100} 50$

Correct answer:

$\dpi{100} 50$

Explanation:

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

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

So $\dpi{100} x=50$

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Example Question #2 :How To Find The Solution To An Equation

Simplify.

-7x +4x-11-x+3

Possible Answers:

-4x-8

-4x-14

4x+8

-4x+8

Correct answer:

-4x-8

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: -7x+4x-x=-4x

2) whole numbers: -11+3=-8

The simplified expression is: -4x-8 .

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Example Question #3 :How To Find The Solution To An Equation

Solve, when x=-2 .

$-6x^{2}+12x+3=$

Possible Answers:

Correct answer:

Explanation:

To solve, insertfor each:

$-6(-2)^{2}+12(-2)+3=$

Simplify:

-6(4)-24+3=

-24-24+3=-45

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

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Example Question #4 :How To Find The Solution To An Equation

Solve for.

$5x^{2}-14=6$

Possible Answers:

Correct answer:

Explanation:

$5(-2)^{2}-14=6$

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Example Question #5 :How To Find The Solution To An Equation

Use the equations to answer the question.

3 + x=4

9+y=13

What is x+y ?

Possible Answers:

Correct answer:

Explanation:

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

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

What story best fits the expression $9\times3$ ?

Possible Answers:

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

Lisa had 9 pencils with two erasers each.

Michelle had 3 stuffed animals and gave 1 away.

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

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 $9\times 3=27$ equation.

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Example Question #7 :How To Find The Solution To An Equation

What isequal to in this equation:

4x+5=13

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.

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Example Question #8 :How To Find The Solution To An Equation

Five more than a number is equal to $\frac{3}{5}$ of twenty-five . What is the number?

Possible Answers:

Correct answer:

Explanation:

From the question, we know thatplus a number equals $\frac{3}{5}$ of. In order to find out what $\frac{3}{5}$ ofis, multiply $\frac{3}{5}$ by $\frac{25}{1}$ .

$\frac{3}{5}\times\frac{25}{1}=\frac{75}{5}$ , 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:

$5+x=\frac{3}{5}\times25$

5+x=15

Subtractfrom both sides of the equation.

x=10

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Example Question #9 :How To Find The Solution To An Equation

Solve for.

2x-2=10

Possible Answers:

x=10

x=12

x=6

x=8

Correct answer:

x=6

Explanation:

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

2x-2=10

Addto both sides of the equation.

2x-2=10

2x=12

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

2x=12

x=6

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

Solve for.

18=3x+3

Possible Answers:

Correct answer:

Explanation:

First, subtract the three from both sides:

$18-3=3x+3\left ( -3\right )$

15=3x

Then, divide by three on both sides:

$\frac{15}{3}=\frac{3x}{3}$

5=x

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Algebraic Concepts

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #1 :How To Find The Solution To An Equation

Example Question #2 :How To Find The Solution To An Equation

Example Question #3 :How To Find The Solution To An Equation

Example Question #4 :How To Find The Solution To An Equation

Example Question #5 :How To Find The Solution To An Equation

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

Example Question #7 :How To Find The Solution To An Equation

Example Question #8 :How To Find The Solution To An Equation

Example Question #9 :How To Find The Solution To An Equation

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

All ISEE Lower Level Quantitative Resources

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