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ISEE Lower Level Math : Algebraic Concepts

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All ISEE Lower Level Math Resources

10 Diagnostic Tests 170 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #111 : How To Find The Solution To An Equation

6x =15

Possible Answers:

x = 2.4

x = 2.5

x = .4

x = 2.6

Correct answer:

x = 2.5

Explanation:

To solve for in the equation

6x = 15

Divide both sides by the coefficient of , which is .

$\frac{6x}{6} = \frac{15}{6}$

$x = 2\frac{1}{2}$

Convert fraction to decimal:

x = 2.5

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Example Question #112 : How To Find The Solution To An Equation

$\frac{23}{x} = 5$

Possible Answers:

x =4.4

x = 4.3

x = 4.6

x= 4.5

Correct answer:

x = 4.6

Explanation:

To solve

$\frac{23}{x} = 5$

$\frac{x}{1} (\frac{23}{x}) = \frac{x}{1} (\frac{5}{1})$

23 = 5x

$\frac{23}{5} = x$

$4\frac{3}{5} = x$

Convert to equivalent fraction with as the denominator.

$4\frac{3}{5} = 4\frac{6}{10}$

Convert to a decimal

$4\frac{6}{10} = 4.6$

x = 4.6 is the correct answer.

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Example Question #113 : Algebraic Concepts

If 7x + 3 = 17 and 2y - 9 = -15 , then what is the product of (x)(y)?

Possible Answers:

Correct answer:

Explanation:

To determine the product of (x)(y) , first solve each equation to get the values of those variables.

7x + 3 = 17

Subtract from both sides of the equation:

7x + 3 - 3 = 17-3

7x = 14

Divide both sides by the coefficient, which is

$\frac{7x}{7} =\frac{14}{7}$

x = 2

2y-9 = -15

Add to both sides of the equation:

2y - 9 + 9 = -15 + 9

2y = -6

Divide both sides of the equation by the coefficient of the variable, which is 2

$\frac{2y}{2} = \frac{-6}{2}$

y = -3

If x = 2 and y = -3

then the product of .

is the correct answer.

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Example Question #113 : How To Find The Solution To An Equation

If y = 3, which of the following number sentences is true?

Possible Answers:

2 (y-2) = 6

4 (y+7) = 40

5y = 9

6y + 4 = 18

Correct answer:

4 (y+7) = 40

Explanation:

In order to find the solution, simply place the value of , which is , in each equation.

$(6) (3) + 4 \neq 18$

$2(3-2) \neq 6$

$5 (3) - 9 \neq -6$

The only equation that is a true numerical statement if y = 3 is

4 (3+7) = 40

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Example Question #114 : How To Find The Solution To An Equation

Jaden has $\$22$ in his piggy bank. What algebraic expressions would be used to determine how much Jaden needs to buy a video game that costs $\$56?$

Possible Answers:

$\$56 + \$22 = x$

$\$22 + x = \$56$

$\$22 x = \$56$

$22 \times 56 = x$

Correct answer:

$\$22 + x = \$56$

Explanation:

Jaden already has $\$22$ of the $\$56.$ The variable would need to represent how much would be added to $22 to reach his goal of $56.

Therefore,

$\$22 + x = \$56$ is the equation that you would use to solve this word problem.

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Example Question #111 : Equations

Solve when x = -2

$2x^{3} -3x +7$

Possible Answers:

Correct answer:

Explanation:

To solve, insert for each variable in the equation.

$2(-2^{3}) - 3(-2) + 7 =$

Using the Order of Operations, PEMDAS, solve the equation. PEMDAS stands for parentheses, exponents, multiplication/division, addition/subtraction. Remember the exponent tells you how many times to multiply the number by itself.

$-2^{3} = (-2) (-2) (-2) = -8$

The subtraction of a negative is the same as adding a positive.

2(-8) +6 + 7 =

-16 + 13 = -3

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Example Question #116 : How To Find The Solution To An Equation

What is the value of in the following equation?

$4 (x-3) = -23 + (3\times 5)$

Possible Answers:

x = -2

x = -1

x = 1

x = 2

Correct answer:

x = 1

Explanation:

To solve:

$4 (x-3) = -23 + (3\times 5)$

First distribute the to the terms inside the parentheses, and then solve using the Order of Operations or PEMDAS (Parentheses, Exponents. Multiplication/Division, Addition/Subtraction):

4x-12 = -23 + 15

4x -12 = -8

4x -12 + 12 = -8 + 12

4x = 4

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

x = 1 is the correct answer.

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Example Question #111 : How To Find The Solution To An Equation

If $\small y=5$ , which of the following number sentences are true?

Possible Answers:

$\small 4y+7=20$

$\small 2\left ( y-2\right )=6$

$\small 5\left ( y+4\right )=42$

$\small 3y-6=19$

Correct answer:

$\small 2\left ( y-2\right )=6$

Explanation:

Replace the variable $\small y$ with $\small 5$ . Then solve using order of operation (PEMDAS).

$\small 2\left ( y-2\right )=6$

$\small 2\left ( 5-2\right )=6$

$\small 5-2=3$

$\small 2\times3=6$

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Example Question #118 : How To Find The Solution To An Equation

Solve for x in the following equation:

2x = 40

Possible Answers:

x = 15

x = 42

x = 20

x = 38

x = 40

Correct answer:

x = 20

Explanation:

To solve for x in this equation, we must get x to stand alone or get x by itself.

In the equation

2x = 40

to get x by itself, we must cancel out the 2 next to it. To cancel it out, we will divide by 2. If we divide on the left side, we must divide on the right. So,

$\frac{2x}{2} = \frac{40}{2}$

x = 20

Therefore, after getting x to stand alone, we can see that x=20 .

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Example Question #119 : How To Find The Solution To An Equation

Solve for a in the following equation:

a - 5 = 2

Possible Answers:

a=2

a=5

a=25

a=3

a=7

Correct answer:

a=7

Explanation:

To solve for a, we want to get a to stand alone or be by itself. To do that, in the equation

a-5=2

we need to cancel out the 5. In this case, we are subtracting 5 on the left side. To cancel it out, we need to add 5. If we add 5 to the left side, we need to add 5 to the right side. So we get

a-5+5=2+5

a+0 = 7

a=7

Therefore, if we solve for a in the equation, we get a=7 .

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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 #111 : How To Find The Solution To An Equation

Example Question #112 : How To Find The Solution To An Equation

Example Question #113 : Algebraic Concepts

Example Question #113 : How To Find The Solution To An Equation

Example Question #114 : How To Find The Solution To An Equation

Example Question #111 : Equations

Example Question #116 : How To Find The Solution To An Equation

Example Question #111 : How To Find The Solution To An Equation

Example Question #118 : How To Find The Solution To An Equation

Example Question #119 : How To Find The Solution To An Equation

All ISEE Lower Level Math Resources

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