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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #25 : One Step Equations With Fractions

Solve:

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

Possible Answers:

$-\frac{1}{2}$

$\frac{2}{3}$

$-\frac{1}{4}$

Correct answer:

$-\frac{1}{2}$

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, subtract $\frac{6}{10}$ from both sides.

$\frac{6}{10}+x -\left(\frac{6}{10}\right)= \frac{1}{10}-\left(\frac{6}{10}\right)$

$x=-\frac{5}{10} =-\frac{1}{2}$

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Example Question #26 : One Step Equations With Fractions

Solve: $\frac{1}{500}x = \frac{1}{5}$

Possible Answers:

$\frac{1}{100}$

1000

100

$\frac{1}{1000}$

Correct answer:

100

Explanation:

In order to solve for x, multiply both sides of the equation by the reciprocal of the coefficient in front of the unknown variable.

When multiplying fractions, multiply the numerators together and multiply the denominators together. After multiplication is done, find common factors in the numerator and denominator to cancel out and completely simplify the fraction.

$\\\frac{1}{500}x \times 500\\\\= \frac{1}{5}\times 500\\\\=\frac{500}{5}\\\\=\frac{5\cdot 100}{5}$

x=100

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Example Question #27 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$\frac{2}{3}$

$\frac{4}{9}$

$\frac{9}{4}$

$\frac{3}{2}$

Correct answer:

$\frac{9}{4}$

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 the unknown variable in this particular case, isolate by multiplying both sides by the reciprocal of the fraction coefficient in front of the .

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

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

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Example Question #81 : One Step Equations

Evaluate: $\frac{x}{3} = 27$

Possible Answers:

$\frac{1}{9}$

$\frac{1}{81 }$

Correct answer:

Explanation:

In order to isolate the variable, multiply three on both sides of the equation.

$\frac{x}{3} \times3 = 27 \times 3$

x=81

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Example Question #29 : One Step Equations With Fractions

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

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{2}$

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.

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

$x = \frac{5}{4}-\frac{3}{4} = \frac{2}{4}$

Reduce the fraction.

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

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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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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #25 : One Step Equations With Fractions

Example Question #26 : One Step Equations With Fractions

Example Question #27 : One Step Equations With Fractions

Example Question #81 : One Step Equations

Example Question #29 : One Step Equations With Fractions

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

All Pre-Algebra Resources

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