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ISEE Middle Level Math : Equations

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

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All ISEE Middle Level Math Resources

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Example Questions

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Example Question #331 : How To Find The Solution To An Equation

If plus 4 squared minus two is equal to nine times seven-thirds, what is the value of ?

Possible Answers:

Correct answer:

Explanation:

The first step is to convert the word problem "x plus 4 squared minus two is equal to nine times seven-thirds" into mathematical terms:

$x+4^{2}-2=9\cdot \frac{7}{3}$

This can be reduced to:

$x+16-2=\frac{63}{3}$

x+14=21

Subtract 14 from each side.

x=7

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Example Question #331 : How To Find The Solution To An Equation

What is the value of if one plus the square root of is equal to six minus the product of one-fourth and eight?

Possible Answers:

$\sqrt{3}$

Correct answer:

Explanation:

The first step is to convert the expression "one plus the square root of is equal to six minus the product of one-fourth and eight" into mathematical terms:

$1+\sqrt{y}=6-\frac{1}{4}\cdot8$

This reduces to:

$1+\sqrt{y}=6-2$

$1+\sqrt{y}=4$

$\sqrt{y}=3$

Squaring both sides gives us:

y=9

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Example Question #332 : How To Find The Solution To An Equation

What is the value of in the equation below?

$\frac{5}{w}\div \frac{1}{3}=\frac{4}{7}$

Possible Answers:

$26\frac{1}{4}$

$25\frac{1}{4}$

Correct answer:

$25\frac{1}{4}$

Explanation:

The first step is to solve the first half of the equation by inverting the second fraction and multiplying by the first fraction.

$\frac{5}{w}\div \frac{1}{3}=\frac{4}{7}$

$\frac{5}{w}\cdot \frac{3}{1}=\frac{4}{7}$

$\frac{15}{w}=\frac{4}{7}$

Multiply each side by .

$15=\frac{4w}{7}$

Multiply each side by .

105=4w

Divide each side by .

$\frac{105}{4}=w$

This reduces to:

$w=25\frac{1}{4}$

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Example Question #331 : Equations

Simplify the expression below:

$4(x-3)+5*(4\div 2)$

Possible Answers:

4x+2

4x-1

4x-2

x-2

Correct answer:

4x-2

Explanation:

$4(x-3)+5*(4\div 2)$

The first step is to apply the distributive property and solve for the expression in parentheses.

4x-12+5* (2)

4x-12+10

4x-2

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Example Question #541 : Algebraic Concepts

What is the value of a in the equation below?

4a-12=3a+36

Possible Answers:

Correct answer:

Explanation:

To solve for 4a-12=3a+36 , the first step is to add to each side.

4a=3a+48

Next, is subtracted from each side. This leaves a=48

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Example Question #332 : Equations

What is the value of in this equation?

$5x^{2}=45$

Possible Answers:

Correct answer:

Explanation:

The first step is to divide each side of the equation by 5.

$5x^{2}=45$

$x^{2}=9$

Next, we take the square root of each side. This results in x=3 .

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Example Question #543 : Algebraic Concepts

Solve for in the equation:

5(x+4)=1

Possible Answers:

$\frac{19}{5}$

$-\frac{19}{5}$

$-\frac{5}{19}$

Correct answer:

$-\frac{19}{5}$

Explanation:

5(x+4)=1

First, apply the distributive property.

5x+20=1

Next, subtract 20 from each side.

5x=-19

Now, divide each side by 5.

$X = -\frac{19}{5}$

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Example Question #331 : How To Find The Solution To An Equation

Solve the following equation for :

2x-18=4

Possible Answers:

x=-5

x=-7

x=2

x=11

Correct answer:

x=11

Explanation:

To solve for a particular variable in an equation, all other constants need to be moved to one side leaving the variable alone on the other side. To do this, perform inverse operations to manipulate the equation.

To solve for , simply isolate it by adding 18 to both sides and then dividing by two.

Thus,

2x-18+18=4+18

2x=22

$\frac{2x}{2}=\frac{22}{2}$

x=11

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Example Question #335 : How To Find The Solution To An Equation

Solve the following equation:

$\frac{1}{4}x+\frac{3}{4}=\frac{9}{4}$

Possible Answers:

Correct answer:

Explanation:

To solve the equation, you must get by itself on one side of the equation.

The first step would be to eliminate the constant $\frac{3}{4}$ which can be done by subtracting it from both sides.

This would result in

$\frac{9}{4}-\frac{3}{4}=\frac{6}{4}$

$\frac{1}{4}x=\frac{6}{4}$ .

Then we must get rid of the $\frac{1}{4}$ so you must undue the multiplication by division on both sides.

$\frac{6}{4}\div \frac{1}{4} or \frac{6}{4}*\frac{4}{1}= 6$

so the final answer is x=6 .

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Example Question #336 : How To Find The Solution To An Equation

Find g, if a,b, and c are all equal to 2

$\frac{1}{g}=\frac{3}{a}+\frac{2}{b}-\frac{4}{c^2}$

Possible Answers:

$g=\frac{3}{2}$

g=0

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

$g=\frac{2}{3}$

Correct answer:

$g=\frac{2}{3}$

Explanation:

Find g, if a,b, and c are all equal to 2

$\frac{1}{g}=\frac{3}{a}+\frac{2}{b}-\frac{4}{c^2}$

To solve this equation, first plug in 2 for each variable:

$\frac{1}{g}=\frac{3}{2}+\frac{2}{2}-\frac{4}{2^2}$

Next, simplify the equation:

$\frac{1}{g}=\frac{5}{2}-\frac{4}{4}=2\frac{1}{2}-1=1\frac{1}{2}$

So, we get:

$\frac{1}{g}=1\frac{1}{2}=\frac{3}{2}$

Next, take the reciprocal of both sides to get our answer:

$g=\frac{2}{3}$

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ISEE Middle Level Math : Equations

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #331 : How To Find The Solution To An Equation

Example Question #331 : How To Find The Solution To An Equation

Example Question #332 : How To Find The Solution To An Equation

Example Question #331 : Equations

Example Question #541 : Algebraic Concepts

Example Question #332 : Equations

Example Question #543 : Algebraic Concepts

Example Question #331 : How To Find The Solution To An Equation

Example Question #335 : How To Find The Solution To An Equation

Example Question #336 : How To Find The Solution To An Equation

All ISEE Middle Level Math Resources

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