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Pre-Algebra : One-Step Equations

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Example Questions

Example Question #22 : One Step Equations With Fractions

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

Possible Answers:

$\frac{1}{9}$

$\frac{4}{81}$

$\frac{81}{4}$

$\frac{9}{4}$

Correct answer:

$\frac{4}{81}$

Explanation:

In order to solve for , isolate the variable by dividing nine on both sides. This is also the same as multiplying both sides by $\frac{1}{9}$ .

$\frac{4}{9} \times \frac{1}{9}= 9x\times \frac{1}{9}$

$x=\frac{4}{81}$

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Example Question #31 : One Step Equations With Fractions

Solve: $\frac{3}{5}x = \frac{3}{7}$

Possible Answers:

$\frac{7}{5}$

$\frac{3}{4}$

$\frac{5}{7}$

$\frac{1}{2}$

Correct answer:

$\frac{5}{7}$

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 unknown variable.

$\frac{3}{5}x \times \frac{5}{3}= \frac{3}{7}\times \frac{5}{3}$

The three in the numerator and in the denominator cancel out and you are left with,

$x = \frac{5}{7}$ .

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Example Question #32 : One Step Equations With Fractions

Solve:

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

Possible Answers:

$\frac{4}{7}$

$-\frac{4}{7}$

$\frac{4}{49}$

$\frac{1}{7}$

Correct answer:

$\frac{4}{7}$

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 solve for , simply add $\frac{2}{7}$ on both sides to isolate the unknown variable.

$x-\frac{2}{7} +\frac{2}{7}= \frac{2}{7}+\frac{2}{7}$

Since the denominators are same, the numerators can be added. The denominators do not change.

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

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Example Question #33 : One Step Equations With Fractions

Solve the equation:

$\frac{7}{3}x= \frac{2}{7}$

Possible Answers:

$\frac{3}{19}$

$\frac{6}{49}$

$\frac{3}{13}$

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

$\frac{6}{49}$

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 by the reciprocal of the coefficient in front of .

$\frac{7}{3}x\times \frac{3}{7}= \frac{2}{7}\times \frac{3}{7}$

$x=\frac{6}{49}$

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Example Question #34 : One Step Equations With Fractions

Solve:

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

Possible Answers:

$\frac{1}{2}$

$\frac{1}{4}$

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.

To isolate the variable, multiply $\frac{2}{7}$ on both sides.

$\frac{7x}{2} \times \frac{2}{7}= 14\times \frac{2}{7}$

$x= \frac{14}{1}\times \frac{2}{7}$

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

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

From here factor the numerator to find values that will cancel and reduce.

$x=\frac{28}{7}=\frac{4\cdot 7}{7}=4$

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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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Pre-Algebra : One-Step Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #22 : One Step Equations With Fractions

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 #34 : One Step Equations With Fractions

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

All Pre-Algebra Resources

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