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Pre-Algebra : Pre-Algebra

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 #821 : Pre Algebra

Solve for :

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

Possible Answers:

$\frac{2}{3}$

$\frac{3}{4}$

Correct answer:

Explanation:

The goal is to isolate the variable on one side.

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

The opposite operation of addition is subtraction so subtract $\frac{1}{2}$ from each side:

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

Simplifying, we get the solution:

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

Finally, reducing to simplest terms:

x = 1

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Example Question #822 : Pre Algebra

Solve for :

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

Possible Answers:

$\frac{5}{2}$

$\frac{21}{4}$

$-\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

The goal is to isolate the variable on one side.

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

The opposite operation of subtraction is addition so add $\frac{7}{4}$ to each side:

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

Simplifying, we get the final solution:

$x = \frac{10}{4}$

Reducing the fraction we obtain the final solution:

$x = \frac{5}{2}$

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Example Question #78 : One Step Equations

Solve for :

$\frac{x}{\frac{3}{4}}=12$

Possible Answers:

12.75

Correct answer:

Explanation:

Explanation:

Isolate the variable to one side.

Multiply each side by $\frac{3}{4}$ :

$\frac{x}{\frac{3}{4}}=12$

$\frac{x\frac{3}{4}}{\frac{3}{4}}=\frac{12}{1}*\frac{3}{4}$

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Example Question #14 : One Step Equations With Fractions

Solve for ""

$\frac{1}{6}x=10$

Possible Answers:

x=60

x=2

x=10

x=40

x=30

Correct answer:

x=60

Explanation:

Because of the fraction, you must mulitply each side by 6, removing the $\frac{1}{6}$ .

$6\left(\frac{1}{6} \right )x=10\cdot6$

1x=60

The problem then reads x=60 .

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Example Question #81 : One Step Equations

Solve for .

4z=10

Possible Answers:

$z=\frac{5}{2}$

z=40

$z=\frac{5}{4}$

z=0

$z=\frac{10}{2}$

Correct answer:

$z=\frac{5}{2}$

Explanation:

To get z by itself, you must divide both sides of the equation by 4

$\frac{4z}{4}=\frac{10}{4}$

which simplifies to

$z=\frac{10}{4}=\frac{5}{2}$

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Example Question #82 : One Step Equations

Solve this equation: $x-\frac{5}{2}=\frac{3}{4}$

Possible Answers:

$x=-\frac{7}{4}$

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

$x=\frac{13}{4}$

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

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

Correct answer:

$x=\frac{13}{4}$

Explanation:

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

Isolate x:

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

Find a common denominator:

$x=\frac{3}{4}+\frac{5}{2}*\frac{2}{2}\rightarrow x=\frac{3}{4}+\frac{10}{4}=\frac{13}{4}$

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Example Question #22 : One Step Equations With Fractions

Solve for :

$\frac{18}{2}x=81$

Possible Answers:

x=5

x=10

x=2.25

x=4.5

x=9

Correct answer:

x=9

Explanation:

Normally when we have a fraction we multiply by the reciprocal to get the fractions to equate to 1. Consider this fraction and its reciprocal $\frac{5}{2}*\frac{2}{5}=1$ . But since our fraction can be reduced to a whole number we can just divide both sides by that number.

$\frac{18}{2}x=81$

Reduce the fraction:

9x=81

Isolate x by dividing both sides by nine:

x=9

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Example Question #81 : One Step Equations

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

Possible Answers:

$\frac{4}{3}$

$\frac{1}{3}$

$\frac{4}{3}$

$\frac{3}{2}$

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Multiply both sides by the reciprocal of the coefficient in front of the in order to isolate the variable.

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

x=3

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Example Question #24 : One Step Equations With Fractions

Solve: $9x = \frac{1}{9}$

Possible Answers:

$\frac{1}{18}$

$\frac{1}{9}$

$\frac{1}{81 }$

Correct answer:

$\frac{1}{81 }$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Divide by nine on both sides to isolate the variable.

$\frac{9x }{9}= \frac{\frac{1}{9}}{9}$

$x=\frac{1}{9}\times\frac{1}{9}=\frac{1}{81}$

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Example Question #271 : Algebraic Equations

Solve:

$\frac{6}{10}+x = \frac{1}{10}$

Possible Answers:

$\frac{2}{3}$

$-\frac{1}{2}$

$-\frac{1}{4}$

Correct answer:

$-\frac{1}{2}$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To isolate the unknown variable, subtract $\frac{6}{10}$ from both sides.

$\frac{6}{10}+x -\left(\frac{6}{10}\right)= \frac{1}{10}-\left(\frac{6}{10}\right)$

$x=-\frac{5}{10} =-\frac{1}{2}$

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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #821 : Pre Algebra

Example Question #822 : Pre Algebra

Example Question #78 : One Step Equations

Example Question #14 : One Step Equations With Fractions

Example Question #81 : One Step Equations

Example Question #82 : One Step Equations

Example Question #22 : One Step Equations With Fractions

Example Question #81 : One Step Equations

Example Question #24 : One Step Equations With Fractions

Example Question #271 : Algebraic Equations

All Pre-Algebra Resources

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