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

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

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All ISEE Lower Level Math Resources

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Example Questions

Example Question #11 : How To Find The Solution To An Equation

Determine the value of .

$-2x^{2} +36 = -14$

Possible Answers:

Correct answer:

Explanation:

To solve, we need to isolate .

$-2x^{2} +36 = -14$

Subtract $\small 36$ from both sides.

-2x^2+36-36=-14-36

-2x^2=-50

Divide both sides by $\small -2$ .

$\frac{-2x^2}{-2}=\frac{-50}{-2}$

x^2=25

Now, take the square root of both sides.

$\sqrt{x^2}=\sqrt{25}$

x=5

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Example Question #12 : How To Find The Solution To An Equation

Simplify the expression.

$-7x^{^{2}}-2x +6x -3 +3x^{2}$

Possible Answers:

$-4x^{2}+4x-3$

$10x^{2} +4x -2$

$4x^{2}-4x-3$

$-4x^{2}-4x-3$

$-4x^{2}+4x+3$

Correct answer:

$-4x^{2}+4x-3$

Explanation:

To simplify, you will need to combine like terms.

First, combine the two terms that have an $x^{2}$ .

$-7x^{2}+3x^{2}=-4x^{2}$

Then combine the two terms that have an .

-2x+6x=4x

Last, put them all together.

$-4x^{2} +4x -3$

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Example Question #13 : How To Find The Solution To An Equation

What value of makes this statement true?

y - 12 = 39

Possible Answers:

y=27

y=41

y=37

y=47

y=51

Correct answer:

y=51

Explanation:

Add 12 to each side:

y - 12 = 39

y - 12 + 12 = 39 + 12

y = 51

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Example Question #14 : How To Find The Solution To An Equation

What value of makes this statement true?

y + 12 = 39

Possible Answers:

y = 17

y = 37

y = 11

y = 27

y = 21

Correct answer:

y = 27

Explanation:

Subtract 12 from both sides:

y + 12 = 39

y + 12 -12 = 39 -12

y = 27

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Example Question #15 : How To Find The Solution To An Equation

Solve for x.

5x-3=12

Possible Answers:

Correct answer:

Explanation:

5x-3=12

Add 3 to both sides.

5x = 12+3

5x=15

Divide both sides by 5.

$\frac{5x}{5}=\frac{15}{5}$

Reduce.

x=5

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Example Question #16 : How To Find The Solution To An Equation

At the grocery store, Sarah bought 3 bags of flour that cost $2 each and a frozen pizza. Her total was $11. Which equation should be used to find the cost of the frozen pizza (p)?

Possible Answers:

2(3)-p=11

3+2+p=11

3+2p=11

3(2)+p=11

Correct answer:

3(2)+p=11

Explanation:

Try to think of the story problem as a math equation.

3 bags of flour cost $2 each: 3 x 2 or 3(2)

One frozen pizza = p

Total = 11

The 3 bags and the frozen pizza are added together to make the total, so the correct answer is: 3(2)+p=11

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Example Question #17 : How To Find The Solution To An Equation

The total combined weight of a dog, cat, and mouse is 12 pounds. If the dog weighs three times as much as the mouse, and the mouse half as much as the cat, how much does the mouse weigh?

Possible Answers:

3 pounds

2 pounds

4 pounds

5 pounds

Correct answer:

2 pounds

Explanation:

1 mouse + 1 cat + 1 dog = 12 pounds

Since we're told how much the cat and dog weigh compared to the mouse, we can recognize:

1 mouse + 2 mice + 3 mice = 12 pounds

Add the mice together:

6 mice = 12 pounds

1 mouse = 12 $\div$ 6 = 2 pounds

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Example Question #18 : How To Find The Solution To An Equation

Simplify:

8y+15-4y-4

Possible Answers:

4y+11

11-4y

15y

12y+19

Correct answer:

4y+11

Explanation:

Combine like terms:

8y-4y=4y

15-4=11

Put them together for the answer:

4y+11

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Example Question #19 : How To Find The Solution To An Equation

4+r=6

7+s=10

What is the sum of r+s ?

Possible Answers:

Correct answer:

Explanation:

First, solve for and :

4+r=6

r=6-4=2

7+s=10

s=10-7=3

Since r=2 and s=3 ,

r+s=2+3=5 .

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Example Question #20 : How To Find The Solution To An Equation

Solve the equation for :

$\frac{4x}{3}=7+x$

Possible Answers:

x=9

x=21

x=42

x=7

x=14

Correct answer:

x=21

Explanation:

$\frac{4x}{3}=7+x$

4x=3(7+x)

4x=21+3x

4x-3x=21

x=21

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All ISEE Lower Level Math Resources

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

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #11 : How To Find The Solution To An Equation

Example Question #12 : How To Find The Solution To An Equation

Example Question #13 : How To Find The Solution To An Equation

Example Question #14 : How To Find The Solution To An Equation

Example Question #15 : How To Find The Solution To An Equation

Example Question #16 : How To Find The Solution To An Equation

Example Question #17 : How To Find The Solution To An Equation

Example Question #18 : How To Find The Solution To An Equation

Example Question #19 : How To Find The Solution To An Equation

Example Question #20 : How To Find The Solution To An Equation

All ISEE Lower Level Math Resources

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