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ISEE Lower Level Math : Algebraic Concepts

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Example Questions

Example Question #71 : Algebraic Concepts

What is the value of a in the equation below?

$3(a-2)=16-(3\cdot 3)$

Possible Answers:

$4\frac{1}{3}$

$3\frac{1}{3}$

Correct answer:

$4\frac{1}{3}$

Explanation:

To solve this equation, the distributive property should be applied to the first part of the equation, and the numbers in the parentheses should be multiplied by each other.

$3(a-2)=16-(3\cdot 3)$

3a-6=16-9

3a-6=7

3a=13

$a=\frac{13}{3}$

$a=4\frac{1}{3}$

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Example Question #71 : Equations

If Elaine is six years younger than twice Jack's age, and Jack is currently 12, how old is Elaine?

Possible Answers:

Correct answer:

Explanation:

If Elaine is six years younger than twice Jack's age, and Jack is currently 12, how old is Elaine?

We must rewrite this word problem in terms of an equation.

The phrase 'six years younger than twice Jack's age' indicates the algebraic expression

2 x Jack's age – 6

If Jack is currently 12, we can simply plug in this value into our expression to get

2 x 12 – 6

Remember "order of operations"! Multiplication comes before subtraction.

24 – 6 =

18.

Elaine is currently 18 years old.

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Example Question #72 : How To Find The Solution To An Equation

Solve for :

$x^{2}\cdot5=120+5$

Possible Answers:

100

125

Correct answer:

Explanation:

$x^{2}\cdot5=120+5$

Simplify the right side of the equation by adding 120 and 5:

$x^{2}\cdot5=125$

Divide each side by 5:

$x^{2}=25$

Take the square root of both sides to isolate :

x=5

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Example Question #72 : Equations

What expression represents 24 more than 4 times k?

Possible Answers:

4(6+k)

6(6+k)

4(4+k)

4(6+k)+2

Correct answer:

4(6+k)

Explanation:

24 more than 4 times k is equal to 4k+24 .

This can then be reduced to 4(6+k) , which is therefore the correct answer.

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Example Question #73 : Equations

Solve for :

$5x-5=3+(4\times 3)$

Possible Answers:

Correct answer:

Explanation:

The first step in solving this equation is the solve for the numbers in parentheses.

$5x-5=3+(4\times 3)$

5x-5=3+12

Add to simplify the right side of the equation.

5x-5=15

Add 5 to each side.

5x-5+5=15+5

5x=20

Divide each side by 5.

$\frac{5x}{5}=\frac{20}{5}$

The left side of the equation cancels.

$x=\frac{20}{5}$

Finally, simplify the right side to solve.

$x=\frac{20}{5}=4$

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Example Question #71 : Equations

What is the value of in the equation below?

3y=5y-8(3-1)

Possible Answers:

Correct answer:

Explanation:

The first step is to solve for the term in parenthesis:

3y=5y-8(3-1)

3y=5y-8(2)

Next we multiply 8 by 2:

3y=5y-16

Next, we subtract from each side:

3y-5y=5y-16-5y

-2y=-16

Now, we divide each side by :

$\frac{-2y}{-2}=\frac{-16}{-2}$

$y=\frac{-16}{-2}=8$

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Example Question #74 : Equations

Solve for in the equation:

x+4=12

Possible Answers:

Correct answer:

Explanation:

x+4=12

To solve, we will need to isolate the variable.

Subtract 4 from each side of the equation.

x+4-4=12-4

x=12-4

x=8

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Example Question #75 : How To Find The Solution To An Equation

If is equal to 2, what is the value of the given expression?

5x(5+4)

Possible Answers:

110

Correct answer:

Explanation:

In order to solve this problem, the first step is to plug in 2 for the value of .

5x(5+4)

x=2

$5\times 2(5+4)$

Next, use order of operations. Solve for the term in parenthesis.

$5\times 2(9)$

Multiply.

$5\times18$

90 is the correct answer.

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Example Question #79 : Algebraic Concepts

Solve for all positive values of :

$4x^{2}-5\cdot6=6$

Possible Answers:

$\sqrt{3}$

Correct answer:

Explanation:

$4x^{2}-5\cdot6=6$

The first step is to multiply 5 by 6:

$4x^{2}-30=6$

Next, add 30 to each side:

$4x^{2}=36$

Divide both sides by 4:

$x^{2}=9$

Take the square root:

x=3 .

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Example Question #75 : Equations

If 6x+2=2y and y=4 , what is the value of ?

Possible Answers:

$\frac{1}{6}$

$\frac{1}{3}$

Correct answer:

Explanation:

If 6x+2=2y and y=4 , the first step is to plug in for .

This results in:

$6x+2=2\cdot4$

6x+2=8

Subtract from each side.

6x=6

Divide each side by 6.

x=1

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All ISEE Lower Level Math Resources

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ISEE Lower Level Math : Algebraic Concepts

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #71 : Algebraic Concepts

Example Question #71 : Equations

Example Question #72 : How To Find The Solution To An Equation

Example Question #72 : Equations

Example Question #73 : Equations

Example Question #71 : Equations

Example Question #74 : Equations

Example Question #75 : How To Find The Solution To An Equation

Example Question #79 : Algebraic Concepts

Example Question #75 : Equations

All ISEE Lower Level Math Resources

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