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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #31 : One Step Equations With Fractions

Solve: $\frac{3}{4} +x =\frac{12}{5}$

Possible Answers:

$\frac{33}{20}$

$\frac{11}{20}$

$\frac{9}{20}$

$\frac{11}{9}$

Correct answer:

$\frac{33}{20}$

Explanation:

Subtract three-fourths from both sides.

$\frac{3}{4} +x -\frac{3}{4}=\frac{12}{5}-\frac{3}{4}$

Find the least common denominator. In this case the LCD is . Reconvert the fractions.

$x=\frac{12}{5}-\frac{3}{4} = \frac{48}{20}- \frac{15}{20} = \frac{33}{20}$

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Example Question #32 : One Step Equations With Fractions

Solve:

$\frac{6}{7} +x = -\frac{8}{7}$

Possible Answers:

$\frac{2}{7}$

$-\frac{2}{7}$

$-\frac{7}{2}$

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.

Substract $\frac{6}{7}$ from both sides of the equation and solve for .

$\frac{6}{7} +x-\frac{6}{7} = -\frac{8}{7}-\frac{6}{7}$

Since both fractions have the same denominator we can simply subtract the numerators.

$x=-\frac{14}{7}=-\frac{2\cdot 7}{7}=-2$

The seven in the numerator and denominator cancel out to reduce the fraction to just negative two.

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Example Question #33 : One Step Equations With Fractions

Solve:

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

Possible Answers:

$\frac{2}{9}$

$\frac{4}{9}$

$\frac{2}{3}$

$\frac{1}{4}$

Correct answer:

$\frac{4}{9}$

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, divide by three on both sides.

This is the same as multiplying one-third on both sides.

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

When multiplying two fractions together, multiply their numerators and then multiply their denominators.

$x=\frac{4}{9}$

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Example Question #91 : One Step Equations

Solve: $\frac{x}{7}= 28$

Possible Answers:

$\frac{1}{4}$

196

Correct answer:

196

Explanation:

To isolate unknown variable, multiply seven on both sides.

$\frac{x}{7}\times 7= 28\times 7$

x=196

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Example Question #35 : One Step Equations With Fractions

Determine the unknown variable:

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

Possible Answers:

$-\frac{7}{9}$

$-\frac{3}{5}$

$-\frac{10}{9}$

$-\frac{1}{2}$

$-\frac{19}{15}$

Correct answer:

$-\frac{10}{9}$

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 the reciprocal of $-\frac{3}{5}$ on both sides to isolate .

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

When multiplying fractions, multiply the numerators together and then multiply the denominators together.

$x= -\frac{10}{9}$

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Example Question #31 : One Step Equations With Fractions

Solve: $3x = \frac{11}{4}$

Possible Answers:

$\frac{11}{12}$

$\frac{33}{4}$

$-\frac{1}{4}$

Correct answer:

$\frac{11}{12}$

Explanation:

Divide on both sides. This is also similar to multiplying both sides by $\frac{1}{3}$ .

$3x \times \frac{1}{3}= \frac{11}{4}\times \frac{1}{3}$

$x= \frac{11}{4}\times \frac{1}{3} = \frac{11}{12}$

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Example Question #41 : One Step Equations With Fractions

Solve: $\frac{7}{9}x = 3$

Possible Answers:

$\frac{3}{7}$

$\frac{7}{3}$

$\frac{7}{27}$

$\frac{27}{7}$

$\frac{1}{21}$

Correct answer:

$\frac{27}{7}$

Explanation:

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

$\frac{7}{9}x \times \frac{9}{7}= 3\times \frac{9}{7}$

By multiplying the reciprocal of the coefficient in front of , we can see that that can be left as a single variable.

Multiply the whole number with the numerator.

$x= 3\times \frac{9}{7} = \frac{27}{7}$

The answer is: $\frac{27}{7}$

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Example Question #41 : One Step Equations With Fractions

Solve for the unknown variable: $\frac{4x}{3} = 9$

Possible Answers:

$\frac{3}{2}$

$\frac{3}{4}$

$\frac{4}{27}$

$\frac{27}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{27}{4}$

Explanation:

To isolate the unknown variable, multiply both sides by $\frac{3}{4}$ , which is the reciprocal of the coefficient in front of the variable.

$\frac{4x}{3} \times \frac{3}{4} = 9\times \frac{3}{4}$

The left side of the equation will become . On the right side of the equation, multiply the integer with the numerator of the fraction.

The answer is:

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

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Example Question #42 : One Step Equations With Fractions

Solve: $\frac{5}{8}x = \frac{7}{9}$

Possible Answers:

$\frac{45}{56}$

$\frac{35}{72}$

$\frac{72}{35}$

$\frac{1}{3}$

$\frac{56}{45}$

Correct answer:

$\frac{56}{45}$

Explanation:

In order to isolate the variable, first multiply both sides by the reciprocal of $\frac{5}{8}$ .

$\frac{5}{8}x \times \frac{8}{5}= \frac{7}{9}\times \frac{8}{5}$

Cancel out the fractions on the left side of the equation.

$x= \frac{7}{9}\times \frac{8}{5}$

For these two fractions, multiply the numerator with the numerator, and the denominator with the denominator.

$x= \frac{7}{9}\times \frac{8}{5}=\frac{56}{45}$

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Example Question #42 : One Step Equations With Fractions

Solve: $\frac{3}{8}x = \frac{7}{6}$

Possible Answers:

$\frac{28}{9}$

$\frac{28}{3}$

$\frac{3}{28}$

$\frac{19}{24}$

$\frac{24}{19}$

Correct answer:

$\frac{28}{9}$

Explanation:

In order to isolate the variable, multiply both sides by the reciprocal of the coefficient in front of the .

$\frac{3}{8}x \times \frac{8}{3}= \frac{7}{6}\times \frac{8}{3}$

Simplify the fractions on the left side.

$x= \frac{7}{6}\times \frac{8}{3}$

Reduce the on the denominator with the in the numerator.

$x= \frac{7}{2 \times 3}\times \frac{2\times 4}{3} = \frac{7\times 4}{3 \times 3} = \frac{28}{9}$

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #31 : One Step Equations With Fractions

Example Question #32 : One Step Equations With Fractions

Example Question #33 : One Step Equations With Fractions

Example Question #91 : One Step Equations

Example Question #35 : One Step Equations With Fractions

Example Question #31 : One Step Equations With Fractions

Example Question #41 : One Step Equations With Fractions

Example Question #41 : One Step Equations With Fractions

Example Question #42 : One Step Equations With Fractions

Example Question #42 : One Step Equations With Fractions

All Pre-Algebra Resources

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