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ISEE Middle Level Math : Algebraic Concepts

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

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6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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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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Example Question #547 : Algebraic Concepts

Solve the following equations when y=5 .

y=2x-3

Possible Answers:

Correct answer:

Explanation:

The first step to solve this equation is to plug in your know variable with the value given, .

Now you have an expression that reads 5=2x-3 and we now solve for .

First you must move the constant by adding to both sides resulting in,

8=2x .

The last step is to divide both sides by resulting in,

x=4 .

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Example Question #541 : Algebraic Concepts

Solve for when x=6 :

$y=\frac{x}{2}+7$

Possible Answers:

Correct answer:

Explanation:

The first is to plug in the value given in the problem leaving us with,

$y=\frac{6}{2}+7$ .

The next step is to complete the division which is

$6\div2=3$ .

Then you add the constant and that gives you an answer of,

3+7=10 .

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Example Question #549 : Algebraic Concepts

Solve for :

9x + 2.3 =-10.3

Possible Answers:

x = -1.4

x = -12.6

x = 1.4

x = 12.6

Correct answer:

x = -1.4

Explanation:

This is a two-step equation. The first step is to isolate the variable. Subtract 2.3 from both sides of the equation:

9x +2.3 -2.3 = -10.3 - 2.3

9x = -12.6

Divide both sides of the equation by the coefficient which is 9:

x = -1.4

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Example Question #550 : Algebraic Concepts

$\frac{1}{2}x + 3 = 5$

Possible Answers:

x = 5

x = 4

x = 0

x = 8

Correct answer:

x = 4

Explanation:

To isolate the variable, subtract 3 from both sides of the equation:

$\frac{1}{2}x + 3-3 = 5-3$

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

Multiply both sides of the equation by the reciprocal of $\frac{1}{2}$ which is $\frac{2}{1}$

$\frac{1}{2}\times(\frac2{}{1}) = 2 \times \frac{2}{1}$

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

x = 4

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ISEE Middle Level Math : Algebraic Concepts

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

All ISEE Middle Level Math Resources

Example Questions

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

Example Question #547 : Algebraic Concepts

Example Question #541 : Algebraic Concepts

Example Question #549 : Algebraic Concepts

Example Question #550 : Algebraic Concepts

All ISEE Middle Level Math Resources

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