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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 #1 : One Step Equations With Fractions

Solve for :

$x + \frac{7}{3} = \frac{1}{6}$

Possible Answers:

$-\frac{13}{6}$

$\frac{13}{6}$

$\frac{8}{3}$

$\frac{8}{6}$

$-\frac{6}{13}$

Correct answer:

$-\frac{13}{6}$

Explanation:

The goal is to isolate the variable on one side.

$x + \frac{7}{3} = \frac{1}{6}$

The opposite operation of addition is subtraction so subtract $\frac{7}{3}$ from each side:

$x + \frac{7}{3} - \frac{7}{3} = \frac{1}{6} - \frac{7}{3}$

In order to complete the subtraction on the right hand side, we must first determine the common denominator, or common multiples of 3 and 6. The least common multiple of 3 and 6 is 6 itself.

$x = \frac{1}{6} - \frac{14}{6}$

Simplifying, we get the final solution:

$x = -\frac{13}{6}$

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Example Question #5 : One Step Equations With Fractions

Solve for :

$x - \frac{5}{6} = \frac{5}{12}$

Possible Answers:

$\frac{7}{12}$

$-\frac{5}{4}$

$\frac{13}{12}$

$\frac{5}{4}$

$\frac{10}{12}$

Correct answer:

$\frac{5}{4}$

Explanation:

The goal is to isolate the variable on one side.

$x - \frac{5}{6} = \frac{5}{12}$

The opposite operation of subtraction is addition so add $\frac{5}{6}$ to each side:

$x - \frac{5}{6} + \frac{5}{6} = \frac{5}{12} + \frac{5}{6}$

In order to complete the addition on the right hand side, we must first determine the common denominator, or common multiples of 6 and 12. The least common multiple of 6 and 12 is 12 itself.

$x = \frac{5}{12} + \frac{10}{12}$

Simplifying, we obtain the solution:

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

Reducing the fraction to its simplest terms we get the final solution:

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

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Example Question #1 : One Step Equations With Fractions

Solve for y

6y=15

Possible Answers:

y=90

$y=\frac{6}{15}$

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

$y=\frac{5}{6}$

y=6

Correct answer:

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

Explanation:

To get y by itself, you must divide by 6 on both sides

$\frac{6y}{6}=\frac{15}{6}$

which simplifies to

$y=\frac{15}{6}=\frac{5}{2}$

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Example Question #5 : One Step Equations With Fractions

Solve for x

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

Possible Answers:

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

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

x=3

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

x=5

Correct answer:

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

Explanation:

To get x by itself, you must multiply both sides of the equation by 5

$\frac{x}{5}\times5=\frac{1}{3}\times5$

which simplifies to

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

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Example Question #2 : One Step Equations With Fractions

Solve the equation below for x:

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

Possible Answers:

$\small \small 25$

$\small 45$

$\small 5$

$\small 125$

$\small 50$

Correct answer:

$\small \small 25$

Explanation:

For this equation, isolate the variable $\small x$ by preforming equivalent operations on both sides of the equation.

To isolate a variable multiplied by a fraction, any fraction multiplied by it's reciprocal equals one.

$\small \left(\frac{5}{1}\right)\small \frac{1}{5}x=5\left(\frac{5}{1}\right)$

Because $\small \frac{5}{5} = 1$ , we isolate $\small x$ , and the equation becomes $\small x=5\cdot \left(\frac{5}{1}\right)$

multiplying the values on the right side gives us

$\small x=\frac{25}{1}= 25$

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Example Question #6 : One Step Equations With Fractions

Solve for n:

$\frac{3}{4}n=9$

Possible Answers:

$n=\frac{33}{4}$

$n=\frac{27}{4}$

n=12

n=6

Correct answer:

n=12

Explanation:

$\frac{3}{4}n=9$

$\frac{4}{3}\left(\frac{3}{4}\cdot n\right)=\left(\frac{4}{3}\right)\left(9 \right )$

$n=\frac{36}{3}=12$

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Example Question #71 : One Step Equations

Solve:

$\frac{6x}{5}= 4$

Possible Answers:

$\frac{20}{6}$

$\frac{24}{5}$

$\frac{10}{3}$

$\frac{30}{4}$

Correct answer:

$\frac{10}{3}$

Explanation:

Eliminate the denominator by multiplying both sides by 5:

$6x=5\cdot 4$

6x=20

Isolate the variable by dividing both sides by 6:

$\frac{6x}{6}=\frac{20}{6}$

$1x=\frac{20}{6}$

Reduce the fraction to it lowest terms by dividing 20 and 6 by 2:

$x= \frac{10}{3}$

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Example Question #72 : One Step Equations

Solve for :

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

Possible Answers:

$x=\frac{8}{3}$

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

$x=\frac{10}{3}$

x=5

Correct answer:

$x=\frac{8}{3}$

Explanation:

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

Divide both sides by $\frac{3}{4}$ :

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

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

Simplify:

$\frac{\frac{6}{3}}{\frac{3}{4}}=\frac{6}{3}\times \frac{4}{3}=\frac{24}{9}=\frac{8}{3}=x$

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Example Question #73 : One Step Equations

Solve for :

$\frac{3}{4}x=36$

Possible Answers:

$\small 16$

$\small 48$

$\small 27$

$\small 18$

$\small 0$

Correct answer:

$\small 48$

Explanation:

To get x by itself multiply both sides by 4 to get

3x=4*36 , then divide both sides by 3 to get

$x=\left(\frac{4*36}{3}\right)$

When you simplify, you can cancel the three on bottom with the 3 in the numerator because it is a factor of 36 leaving you with:

x=4*12

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Example Question #11 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$\frac{16}{9}$

$\frac{3}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{16}{9}$

Explanation:

The goal is to isolate x so to solve this you will first multiple both sides by 4

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

This gives you:

$3x=\frac{16}{3}$

You must then divide both sides by 3

$\frac{3x}{3}=\frac{16}{3}*\frac{1}{3}$

you then get your answer:

$x=\frac{16}{9}$

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : One Step Equations With Fractions

Example Question #5 : One Step Equations With Fractions

Example Question #1 : One Step Equations With Fractions

Example Question #5 : One Step Equations With Fractions

Example Question #2 : One Step Equations With Fractions

Example Question #6 : One Step Equations With Fractions

Example Question #71 : One Step Equations

Example Question #72 : One Step Equations

Example Question #73 : One Step Equations

Example Question #11 : One Step Equations With Fractions

All Pre-Algebra Resources

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