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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #43 : One Step Equations With Fractions

Solve: $\frac{2}{7}x = 3$

Possible Answers:

$\frac{2}{21}$

$\frac{7}{6}$

$\frac{23}{7}$

$\frac{6}{7}$

$\frac{21}{2}$

Correct answer:

$\frac{21}{2}$

Explanation:

In order to isolate the variable, multiply the reciprocal of $\frac{2}{7}$ on both sides of the equation.

$\frac{2}{7}x \times \frac{7}{2}= 3\times \frac{7}{2}$

Simplify the fractions on the left side of the equation.

$x= 3\times \frac{7}{2}$

Multiply the three with the seven on the right side of the equation.

$x= 3\times \frac{7}{2} = \frac{21}{2}$

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Example Question #44 : One Step Equations With Fractions

Solve for in the following equation.

$\frac{x}{4} = 8$

Possible Answers:

x = 4

x = 2

x = 32

x = 12

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

Correct answer:

x = 32

Explanation:

$\frac{x}{4} = 8$

When solving for x, we need to get x alone. To do that, we need to multiply both sides by 4.

$\frac{x}{4} * 4 = 8 * 4$

Multiply through.

$\frac{4x}{4} = 32$

Simplify.

$\frac{1x}{1} = 32$

Solution.

x = 32

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Example Question #45 : One Step Equations With Fractions

Find the solution for g.

$g - \frac{3}{4} = \frac{3}{4}$

Possible Answers:

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

g= 1

$\frac{6}{8}$

$g = \frac{6}{4}=\frac{3}{2}$

g= 0

Correct answer:

$g = \frac{6}{4}=\frac{3}{2}$

Explanation:

This is a simple one-step equation. The objective is to solve for g and isolate it on the right side.

The steps are as follows:

$g-\frac{3}{4}+\frac{3}{4}=\frac{3}{4}+\frac{3}{4}$

$g = \frac{3}{4}+\frac{3}{4}=\frac{6}{4}=\frac{3}{2}$

You can check your answer by inserting g into the original equation as follows.

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

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

It works!

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Example Question #46 : One Step Equations With Fractions

Solve for in the following equation:

$x + \frac{1}{2} = \frac{3}{4}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{2}$

$-\frac{1}{4}$ $\frac{4}{6}$

$\frac{2}{2}$

Correct answer:

$\frac{1}{4}$

Explanation:

When solving for x, we want to get x to stand alone. We subtract $\frac{1}{2}$ from both sides. We get

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

We must find a common denominator. In this case, the lowest common denominator is 4. So we get

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

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

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Example Question #47 : One Step Equations With Fractions

Solve for in the following equation:

$-\frac{2}{3} + x = \frac{4}{5}$

Possible Answers:

$\frac{6}{15}$

$\frac{22}{15}$

$\frac{6}{8}$

$\frac{2}{15}$

$\frac{2}{8}$

Correct answer:

$\frac{22}{15}$

Explanation:

When solving for x, we must get x to stand by itself. Therefore, in the equation

$-\frac{2}{3} + x = \frac{4}{5}$

we will add $\frac{2}{3}$ to both sides. We get

$-\frac{2}{3} + x + \frac{2}{3} = \frac{4}{5} + \frac{2}{3}$

$x = \frac{4}{5} + \frac{2}{3}$

To add the fractions, we must find a common denominator.

In this case, it's 15.

So,

$x = \frac{12}{15} + \frac{10}{15}$

$x = \frac{22}{15}$

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Example Question #44 : One Step Equations With Fractions

Solve for a in the following equation:

$\frac{2}{3} + a = \frac{1}{2}$

Possible Answers:

$a = \frac{7}{6}$

$a = \frac{-1}{-1}$

$a = -\frac{1}{6}$

$a = \frac{3}{5}$

$a = \frac{1}{6}$

Correct answer:

$a = -\frac{1}{6}$

Explanation:

When solving for a, we want to get a by itself. So in the equation,

$\frac{2}{3} + a = \frac{1}{2}$

we must subtract $\frac{2}{3}$ from both sides. We get

$\frac{2}{3} + a - \frac{2}{3} = \frac{1}{2} - \frac{2}{3}$

$a = \frac{1}{2} - \frac{2}{3}$

When subtracting fractions, we need to find a common denominator. In this case, it's 6. So,

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

Now, we subtract the numerators and get

$a = - \frac{1}{6}$

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Example Question #51 : One Step Equations With Fractions

Solve the following equation:

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

Possible Answers:

$x=\frac{3}{25}$

x=15

x=3

$x=\frac{8}{5}$

None of the above.

Correct answer:

x=3

Explanation:

This is a one-step problem in which you need to multiply both sides by to isolate "x."

You will then get:

$x=\frac{3}{5}*5$

The fives cancel and you are left with:

x=3

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Example Question #1 : How To Solve One Step Equations With Fractions In Pre Algebra

Solve for .

$p-\frac{2}{5}=3$

Possible Answers:

p=4

p=3

$p=\frac{13}{5}$

$p=\frac{17}{5}$

Correct answer:

$p=\frac{17}{5}$

Explanation:

Perform the same operation on both sides of the equation.

$p-\frac{2}{5}=3$

It will be easier to write the right side of the equation as a fraction.

$3=\frac{15}{5}$

$p-\frac{2}{5}=\frac{15}{5}$

Now, we add two-fifths to both sides of the equation.

$p-\frac{2}{5}+\frac{2}{5}=\frac{15}{5}+\frac{2}{5}$

$p=\frac{17}{5}$

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Example Question #1 : One Step Equations With Decimals

Solve for :

0.75x=9

Possible Answers:

9.75

Correct answer:

Explanation:

The goal is to isolate the variable on one side.

0.75x=9

Divide each side by 0.75 :

$\frac{0.75x}{0.75}=\frac{9}{0.75 }$

x=12

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Example Question #2 : One Step Equations With Decimals

Solve for :

9.25x=74

Possible Answers:

Correct answer:

Explanation:

The goal is to isolate the variable on one side.

9.25x=74

Divide each side by 9.25 :

$\frac{9.25x}{9.25}=\frac{74}{9.25}$

x=8

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #43 : One Step Equations With Fractions

Example Question #44 : One Step Equations With Fractions

Example Question #45 : One Step Equations With Fractions

Example Question #46 : One Step Equations With Fractions

Example Question #47 : One Step Equations With Fractions

Example Question #44 : One Step Equations With Fractions

Example Question #51 : One Step Equations With Fractions

Example Question #1 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #1 : One Step Equations With Decimals

Example Question #2 : One Step Equations With Decimals

All Pre-Algebra Resources

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