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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #28 : Two Step Equations With Fractions

Solve: $\frac{3}{4}x +\frac{3}{4}= \frac{7}{8}$

Possible Answers:

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{8}{21}$

$\frac{5}{2}$

Correct answer:

$\frac{1}{6}$

Explanation:

Subtract $\frac{3}{4}$ on both sides of the equation.

$\frac{3}{4}x +\frac{3}{4}-\frac{3}{4}= \frac{7}{8}-\frac{3}{4}$

Simplify the left side of the equation.

$\frac{3}{4}x= \frac{7}{8}-\frac{3}{4}$

The numerators on the right side of the equation cannot be subtracted unless both denominators are the same. The least common denominator is . Multiply both the numerator and denominator of $\frac{3}{4}$ by two to get the common denominator.

$\frac{3}{4}x= \frac{7}{8}-\frac{3(2)}{4(2)}$

$\frac{3}{4}x= \frac{7}{8}-\frac{6}{8}$

Subtract the numerators on the right side of the equation.

$\frac{3}{4}x= \frac{1}{8}$

Multiply the reciprocal of $\frac{3}{4}$ , or $\frac{4}{3}$ , in order to isolate .

$\frac{3}{4}x \times \frac{4}{3}= \frac{1}{8}\times \frac{4}{3}$

Simplify both sides.

$x= \frac{1}{8}\times \frac{4}{3} = \frac{4}{24} = \frac{1}{6}$

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Example Question #24 : Two Step Equations With Fractions

$8 \left(\frac{1}{2}x + 6\right) = 24$

Possible Answers:

x = -8

x = 12

x = 8

x = 6

x = -6

Correct answer:

x = -6

Explanation:

$8 \left(\frac{1}{2}x + 6\right) = 24$

Use the distributive Property first to distribute the eight to both terms within the parentheses.

$\left(8 * \frac{1}{2}x\right) + (8 * 6) = 24$

Simplify from here.

First subtract 48 from both sides.

(4x) + (48) = 24

Now divide by four to isolate and solve for x.

$\frac{4x}{4} = \frac{-24}{4}$

x = - 6

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Example Question #31 : Two Step Equations With Fractions

Find the solution for s.

$\frac{3}{6}+\frac{2}{3}s=\frac{3}{5}$

Possible Answers:

$s=\frac{18}{15}$

$s=\frac{6}{4}$

$s=\frac{3}{20}$

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

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

Correct answer:

$s=\frac{3}{20}$

Explanation:

This is a two-step equation. The first step is as follows:

$\frac{3}{6}-\frac{3}{6}+\frac{2}{3}s=\frac{3}{5}-\frac{3}{6}$

$\frac{2}{3}s=\frac{3}{5}-\frac{3}{6} \Rightarrow\frac{2}{3}s=\frac{18}{30}-\frac{15}{30}\Rightarrow \frac{2}{3}s=\frac{3}{30}$

Now we divide both sides by 2/3 as follows:

$\frac{\frac{2}{3}s}{\frac{2}{3}}=\frac{\frac{3}{30}}{\frac{2}{3}}$

$s=\frac{\frac{3}{30}}{\frac{2}{3}}\Rightarrow s=\frac{3}{30}\cdot \frac{3}{2}$

$s= \frac{9}{60}=\frac{3}{20}$

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Example Question #91 : Two Step Equations

$\frac{2}{3}m = 12$

Possible Answers:

m = 8

m = 18

m = 14

m = 36

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

Correct answer:

m = 18

Explanation:

To solve the equation,

$\frac{2}{3}m = 12$

use inverse operations.

Multiply both sides by ,

2m = 36

Divide both sides by ,

m = 18

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Example Question #33 : Two Step Equations With Fractions

Simplify the following

$\frac{3}{5}x=\frac{9}{5}$

Possible Answers:

x=9

x=10

x=3

x=5

x=2

Correct answer:

x=3

Explanation:

This is a two-step problem where you need to isolate x.

The first step is to multiply everything by , which gives you:

3x=9 because the fives on both sides will cancel.

The next and last step is to divide both sides by which gives you a final answer of:

x=3

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Example Question #31 : Two Step Equations With Fractions

$3\frac{5}{8}+4\frac{1}{2}= ?$

The answer must be a mixed number.

Possible Answers:

$11\frac{7}{8}$

$\frac{65}{8}$

$4\frac{5}{8}$

$8\frac{1}{8}$

Correct answer:

$8\frac{1}{8}$

Explanation:

The first step to adding mixed numbers is to convert them into improper fractions.

$3\frac{5}{8}=\frac{[(3\times8)+5]}{8} = \frac{29}{8}$

$4\frac{1}{2}=\frac{[(4\times2)+1]}{2}=\frac{9}{2}$

Next, find the least common multiple of 2 and 8 so that both fractions have the same denominator.

$\frac{9}{2}\times\frac{4}{4}=\frac{36}{8}$

Now that the denominators of both fractions are the same, add the fractions.

$\frac{29}{8}+\frac{36}{8}=\frac{65}{8}$

Convert the improper fraction back into a mixed number.

65 divided by 8 is 8 remainder 1, or $8\frac{1}{8}$ .

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Example Question #31 : Two Step Equations With Fractions

$3\frac{5}{8}+4\frac{1}{2}= ?$

The answer must be a mixed number.

Possible Answers:

$11\frac{7}{8}$

$\frac{65}{8}$

$4\frac{5}{8}$

$8\frac{1}{8}$

Correct answer:

$8\frac{1}{8}$

Explanation:

The first step to adding mixed numbers is to convert them into improper fractions.

$3\frac{5}{8}=\frac{[(3\times8)+5]}{8} = \frac{29}{8}$

$4\frac{1}{2}=\frac{[(4\times2)+1]}{2}=\frac{9}{2}$

Next, find the least common multiple of 2 and 8 so that both fractions have the same denominator.

$\frac{9}{2}\times\frac{4}{4}=\frac{36}{8}$

Now that the denominators of both fractions are the same, add the fractions.

$\frac{29}{8}+\frac{36}{8}=\frac{65}{8}$

Convert the improper fraction back into a mixed number.

65 divided by 8 is 8 remainder 1, or $8\frac{1}{8}$ .

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Example Question #1 : Two Step Equations With Decimals

Solve for :

0.33x+1.66=9.99

Possible Answers:

$25.\overline{42}$

$-25.\overline{42}$

$25.\overline{24}$

$-25.\overline{24}$

Correct answer:

$25.\overline{24}$

Explanation:

The goal is to isolate the variable to one side.

0.33x+1.66=9.99

Subtract 1.66 from both sides:

0.33x+1.66-1.66=9.99-1.66

0.33x=8.33

Divide each side by 0.33 :

$\frac{0.33x}{0.33}=\frac{8.33}{0.33}$

$x=25.\overline{24}$

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Example Question #2 : Two Step Equations With Decimals

Solve for :

.5x+.08=1.68

Possible Answers:

3.28

3.44

3.2

Correct answer:

3.2

Explanation:

Step 1: Subtract from both sides:

.5x+.08-.08=1.68-.08

.5x+0=1.6

.5x=1.6

Step 2: Divide both sides by :

$\frac{.5x}{.5}= \frac{1.6}{.5}$

x=3.2

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Example Question #1 : Two Step Equations With Decimals

Solve for p:

1.5p+0.25=3.25

Possible Answers:

p=2

p=3

p=2.5

p=3.5

Correct answer:

p=2

Explanation:

1.5p+0.25=3.25

1.5p+0.25-0.25=3.25-0.25

1.5p=3.0

$\frac{1.5p}{1.5}=\frac{3.0}{1.5}$

p=2

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #28 : Two Step Equations With Fractions

Example Question #24 : Two Step Equations With Fractions

Example Question #31 : Two Step Equations With Fractions

Example Question #91 : Two Step Equations

Example Question #33 : Two Step Equations With Fractions

Example Question #31 : Two Step Equations With Fractions

Example Question #31 : Two Step Equations With Fractions

Example Question #1 : Two Step Equations With Decimals

Example Question #2 : Two Step Equations With Decimals

Example Question #1 : Two Step Equations With Decimals

All Pre-Algebra Resources

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