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

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All ISEE Middle Level Math Resources

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Example Questions

Example Question #91 : How To Find The Solution To An Equation

Simplify:

(3^2)^8=

Possible Answers:

3^1^0

3^1^8

3^1^6

3^4^8

Correct answer:

3^1^6

Explanation:

When we have an exponent raised to an exponent, our rule is to multiply the exponent by the exponent. Lets look at an easier problem to show this rule.

(2^2)^2

In this problem it is saying two squared, times two squared correct? (Yes)

So what is 2 squared? (4), what is 2 squared again? (4).

So this problem is saying $4\times 4$ which is . This is one way we can do the equation. Another is a rule that was mentioned before. When we have an exponent raised by an exponent *only in these cases* we can multiply the exponents by each other.

So in our easier example the exponent (2) times the other exponent (2) .

Looks like this

$2^{2\times 2}= 2^4$

Or the same thing as saying

$2\times 2\times 2\times 2=16$ . Either way we get the same answer!

Returning back to the original problem. We have the exponent 2 raised to the exponent 8. We can multiply them by each other in this case. $2\times 8=16$

So as the question asks us to simplify we just need to put 3^1^6

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Example Question #91 : How To Find The Solution To An Equation

Solve for .

3n+4=7

Possible Answers:

n=1

n=3

n=4

n=2

Correct answer:

n=1

Explanation:

3n+4=7

3n+4-4=7-4

3n=3

$\frac{3n}{3}=\frac{3}{3}$

n=1

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Example Question #92 : How To Find The Solution To An Equation

Solve for .

$\frac{9}{x}=2$

Possible Answers:

x=3.5

x=4.5

x=4

x=5

Correct answer:

x=4.5

Explanation:

$\frac{9}{x}=2$

9=2x

$\frac{9}{2}=\frac{2x}{2}$

4.5=x

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Example Question #94 : Equations

Solve for .

3q-3=-6

Possible Answers:

q=-2

q=-1

q=2

q=1

Correct answer:

q=-1

Explanation:

3q-3=-6

3q-3+3=-6+3

3q=-3

$\frac{3q}{3}=\frac{-3}{3}$

q=-1

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Example Question #95 : Equations

Solve for :

5t - 17 = 78

Possible Answers:

t = 17

t = 19

t = 21

t = 16

Correct answer:

t = 19

Explanation:

5t - 17 = 78

5t - 17 + 17= 78+ 17

5t = 95

$5t \div 5 = 95 \div 5$

t = 19

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Example Question #96 : Equations

Solve for :

x (x-6) = 40

Possible Answers:

$x = -4 \textrm{ or }x = 10$

$x = 8 \textrm{ or }x = -5$

$x = -8 \textrm{ or }x = 5$

$x = 4 \textrm{ or }x = -10$

Correct answer:

$x = -4 \textrm{ or }x = 10$

Explanation:

Rewrite in standard form:

x (x-6) = 40

$x \cdot x-x \cdot 6 = 40$

$x ^{2}-6x = 40$

$x ^{2}-6x- 40 = 40 - 40$

$x ^{2}-6x- 40 = 0$

Factor the quadratic expression as (x + ?)(x + ?) , replacing the question marks with two integers whose product is and whose sum is . The integers are -10, 4 , so we write the equation as

(x -10)(x + 4) = 0

Set each linear binomial to 0 and solve:

$x - 10 = 0\Rightarrow x = 10$

$x + 4 = 0\Rightarrow x = -4$

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Example Question #97 : Equations

Solve for :

-6x + 13 > 78

Possible Answers:

$x > 10 \frac{5}{6}$

$x < 10 \frac{5}{6}$

$x > -10 \frac{5}{6}$

$x < -10 \frac{5}{6}$

Correct answer:

$x < -10 \frac{5}{6}$

Explanation:

-6x + 13 > 78

-6x + 13 - 13 > 78- 13

-6x > 65

$-6x \div (-6) < 65 \div (-6)$

Note: switch the symbol when dividing by a negative number

$x < -10 \frac{5}{6}$

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Example Question #901 : Concepts

Solve for :

$- \frac{6}{5}y > -\frac{9}{20}$

Possible Answers:

$y< - \frac{3}{8}$

$y< \frac{3}{8}$

$y> - \frac{3}{8}$

$y> \frac{3}{8}$

Correct answer:

$y< \frac{3}{8}$

Explanation:

$- \frac{6}{5}y > -\frac{9}{20}$

$- \frac{5}{6} \left ( - \frac{6}{5} y \right )< - \frac{5}{6} \left ( -\frac{9}{20} \right )$

Note: switch the symbol when dividing by a negative number

$y< \frac{5}{6} \cdot \frac{9}{20}$

$y< \frac{1}{2} \cdot \frac{3}{4}$

$y< \frac{3}{8}$

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Example Question #292 : Algebra

Solve for :

6 (t - 0.13 ) = 9

Possible Answers:

t = 1.47

t = 1.63

t = 1.52

t = 1.37

Correct answer:

t = 1.63

Explanation:

Distribute, then solve:

6 (t - 0.13 ) = 9

$6 \cdot t - 6 \cdot 0.13 = 9$

6 t - 0.78 = 9

6 t - 0.78 + 0.78 = 9+ 0.78

6 t = 9.78

$6 t \div 6 = 9.78 \div 6$

t = 1.63

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Example Question #293 : Algebra

Solve for :

10 - 0.4t = 8.11

Possible Answers:

t = 4.725

t = -4.725

t = 45.275

t = - 45.275

Correct answer:

t = 4.725

Explanation:

10 - 0.4t = 8.11

10 - 0.4t - 10 = 8.11- 10

-0.4t = - ( 10.00 - 8.11 )

-0.4t = - 1.89

$0.4t \div 0.4 = - 1.89 \div \left ( -0.4 \right )$

$t = 1.89 \div 0.4$

Move each decimal point one digit right:

$t = 18.9 \div 4 = 4.725$

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

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #91 : How To Find The Solution To An Equation

Example Question #91 : How To Find The Solution To An Equation

Example Question #92 : How To Find The Solution To An Equation

Example Question #94 : Equations

Example Question #95 : Equations

Example Question #96 : Equations

Example Question #97 : Equations

Example Question #901 : Concepts

Example Question #292 : Algebra

Example Question #293 : Algebra

All ISEE Middle Level Math Resources

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