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ISEE Lower Level Math : Algebraic Concepts

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

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Example Questions

Example Question #61 : How To Find The Solution To An Equation

What is the value of ?

2x=38-8

Possible Answers:

Correct answer:

Explanation:

To solve, we will need to isolate the variable, . Start by solving the right side of the equation.

2x=38-8

2x=30

Next, divide both sides of the equation by 2.

$\frac{2x}{2}=\frac{30}{2}$

The left side of the equation simplifies.

$x=\frac{30}{2}$

Reduce the fraction on the right side of the equation to get the final answer.

$x=\frac{30}{2}=15$

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Example Question #61 : How To Find The Solution To An Equation

Solve for .

5x-25=10

Possible Answers:

x=5

x=4

x=8

x=9

x=7

Correct answer:

x=7

Explanation:

To solve, the first step is to isolate the by adding 25 to each side.

5x-25=10

5x-25+25=20+25

5x=35

Next, each side should be divided by 5.

$5x\div5=35\div5$

x=7

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Example Question #62 : How To Find The Solution To An Equation

What is the value of in the equation?

3y=4y-4(3-1)

Possible Answers:

None of these

Correct answer:

Explanation:

This question largely relies on order of operations.

To solve this equation, the first step is to solve for the value in parenthesis:

3y=4y-4(3-1)

3y=4y-4(2)

Next, multiply 4 by 2.

3y=4y-8

Next, subtract from each side of the equation.

3y-4y=4y-8-4y

-y=-8

Now, multiple each side by . This results in:

-(-y)=-(-8)

y=8

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Example Question #63 : How To Find The Solution To An Equation

Find the value of .

5=w(3-5)+7

Possible Answers:

Correct answer:

Explanation:

To solve for this equation, the first step is to solve for the numbers in the parentheses.

5=w(3-5)+7

This gives us:

5=w(-2)+7

5=-2w+7

Subtract 7 from each side to isolate the variable.

5-7=-2w-7

-2=-2w

Finally, divide by . This will cancel on the right side to get the variable alone.

$\frac{-2}{-2}=\frac{-2w}{-2}$

$\frac{-2}{-2}=w$

Any number divided by itself is equal to 1.

1=w

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Example Question #64 : How To Find The Solution To An Equation

What is the value of in the equation below?

$2 (y+7) = 3 \times (5+3)$

Possible Answers:

Correct answer:

Explanation:

$2 (y+7) = 3 \times (5+3)$

First, the distributive property should be applied on the left side of the equation, and the order of operations should be applied to the left side.

$(2\times y)+(2\times7)=3\times(8)$

2y+14=24

Next, subtract 14 from each side

2y = 10

Now, divide each side by 2.

$\frac{2y}{2}=\frac{10}{2}$

$y=\frac{10}{2}=5$

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Example Question #65 : How To Find The Solution To An Equation

What is the value of in the equation?

$\frac{y}{4} +11 = 39$

Possible Answers:

108

112

Correct answer:

112

Explanation:

$\frac{y}{4} +11 = 39$

The first step is to subtract 11 from each side:

$\frac{y}{4} +11-11 = 39-11$

$\frac{y}{4} = 28$

Now, multiple each side by 4:

$\frac{y}{4}\times4 = 28\times4$

y = 112

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Example Question #66 : How To Find The Solution To An Equation

Solve for in the equation:

$\frac{2}{3x}=\frac{4}{3}$

Possible Answers:

$\frac{1}{4}$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{12}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

$\frac{2}{3x}=\frac{4}{3}$

First, cross multiply in order to simplify the equation:

$\frac{2}{3x}=\frac{4}{3}\rightarrow2\times3=4\times3x$

6=12x

Next, divide each side by 12.

$\frac{6}{12}=\frac{12x}{12}$

$\frac{6}{12}=x$

Simplify.

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

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Example Question #67 : How To Find The Solution To An Equation

Find the value of :

w-3=6(w-2)

Possible Answers:

$-\frac{5}{9}$

$\frac{5}{9}$

None of these

$\frac{9}{5}$

$-\frac{9}{5}$

Correct answer:

$\frac{9}{5}$

Explanation:

The first step to solve this question is to apply the distributive property on the right side.

w-3=6(w-2)

$w-3=(6\times w)-(6\times2)$

w-3=6w-12

Next, add 3 to each side.

w-3+3=6w-12+3

w=6w-9

Next, subtract from each side.

w-6w=6w-9-6w

-5w=-9

Now divide each side by .

$w=\frac{-9}{-5}=\frac{9}{5}$

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Example Question #61 : Equations

What is the value of x in the equation below?

$\frac{9}{x}+8=11$

Possible Answers:

Correct answer:

Explanation:

To solve the equaton below, 8 must be subtracted from each side.

$\frac{9}{x}+8=11$

$\frac{9}{x}=3$

If 9 is divided by 3, the result will be 3. Therefore, the correct answer is that x is equal to 3.

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Example Question #62 : Algebraic Concepts

What is the value of $c\cdot d$ given the expressions below?

$c=2\cdot3$

d-1=1

Possible Answers:

Correct answer:

Explanation:

In order to solve for the value of $c\cdot d$ , the value of c and d must be solved for first.

$c=2\cdot3$

c=6

d-1=1

Here, 1 must be added to each side of the equation.

d=2

Thus, $c\cdot d$ is equal to $6\cdot1=12$ .

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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 #61 : How To Find The Solution To An Equation

Example Question #61 : How To Find The Solution To An Equation

Example Question #62 : How To Find The Solution To An Equation

Example Question #63 : How To Find The Solution To An Equation

Example Question #64 : How To Find The Solution To An Equation

Example Question #65 : How To Find The Solution To An Equation

Example Question #66 : How To Find The Solution To An Equation

Example Question #67 : How To Find The Solution To An Equation

Example Question #61 : Equations

Example Question #62 : Algebraic Concepts

All ISEE Lower Level Math Resources

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