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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #75 : One Step Equations

Solve for :

$\small \frac{3}{5}x=12$

Possible Answers:

$\small \frac{36}{5}$

$\small 12$

$\small \frac{3}{5}$

$\small 20$

$\small 16$

Correct answer:

$\small 20$

Explanation:

To solve this equation, isolate on one side.

First, move the fraction to the other side by multiplying by its reciprocal.

$\small \frac{5}{3}*\frac{3}{5}x = \frac{12}{1}*\frac{5}{3}$

$\small x = \frac{60}{3}$

Next, simplify the complex fraction.

$\small x=20$

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Example Question #11 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$\frac{3}{4}$

$\frac{2}{3}$

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 #12 : One Step Equations With Fractions

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 #79 : One Step Equations

Solve for ""

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

Possible Answers:

x=10

x=40

x=60

x=2

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 #23 : One Step Equations With Fractions

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

Possible Answers:

$\frac{3}{2}$

$\frac{4}{3}$

$\frac{1}{3}$

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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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #75 : One Step Equations

Example Question #11 : One Step Equations With Fractions

Example Question #12 : One Step Equations With Fractions

Example Question #78 : One Step Equations

Example Question #79 : One Step Equations

Example Question #81 : One Step Equations

Example Question #82 : One Step Equations

Example Question #22 : One Step Equations With Fractions

Example Question #23 : One Step Equations With Fractions

Example Question #24 : One Step Equations With Fractions

All Pre-Algebra Resources

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