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Pre-Algebra : Two-Step Equations with Fractions

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Example Questions

Example Question #21 : Two Step Equations With Fractions

Solve: $\frac{2}{9}-x = \frac{7}{9}$

Possible Answers:

$\frac{14}{9}$

$\frac{5}{18}$

$-\frac{5}{18}$

$\frac{5}{9}$

$-\frac{5}{9}$

Correct answer:

$-\frac{5}{9}$

Explanation:

Add on both sides of the equation.

$\frac{2}{9}-x +x= \frac{7}{9}+x$

$\frac{2}{9}= \frac{7}{9}+x$

Subtract $\frac{7}{9}$ from both sides of the equation.

$\frac{2}{9}- \frac{7}{9}=x$

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

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Example Question #81 : Two Step Equations

Solve: $\frac{4}{x} = 16$

Possible Answers:

$\frac{1}{20}$

$\frac{1}{4}$

$\frac{1}{64}$

Correct answer:

$\frac{1}{4}$

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 isolate , multiply by by both sides on the equation.

$\frac{4}{x} \times x= 16\times x$

4=16x

Divide by 16 on both sides of the equation.

$\frac{4}{16}=\frac{16x}{16}$

$x=\frac{4}{16}=\frac{1}{4}$

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Example Question #21 : Two Step Equations With Fractions

Solve:

$\frac{3}{4x} +1= 16$

Possible Answers:

$\frac{4}{45}$

$\frac{1}{40}$

$\frac{1}{20}$

$\frac{45}{4}$

Correct answer:

$\frac{1}{20}$

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.

The objective is to isolate . Subtract one from both sides of the equation.

$\frac{3}{4x} +1-1= 16-1$

$\frac{3}{4x} = 15$

Multiply by on both sides of the equation.

$\frac{3}{4x} \times 4x= 15\times 4x$

3=60x

Divide by sixty on both sides.

$x= \frac{3}{60} = \frac{1}{20}$

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Example Question #141 : Algebraic Equations

Solve: $\frac{1}{3} -x = \frac{1}{7}$

Possible Answers:

$\frac{4}{21}$

$-\frac{1}{4}$

$-\frac{7}{4}$

$-\frac{4}{21}$

$\frac{1}{4}$

Correct answer:

$\frac{4}{21}$

Explanation:

Add on both sides of the equation.

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

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

Subtract $\frac{1}{7}$ on both sides.

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

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

$\frac{7}{21}-\frac{3}{21}=x$

$x=\frac{4}{21}$

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Example Question #24 : Two Step Equations With Fractions

Solve: $\frac{3}{x} = \frac{1}{6}$

Possible Answers:

$\frac{1}{18}$

$\frac{1}{2}$

Correct answer:

Explanation:

Multiply by on both sides of the equation.

$\frac{3}{x} \times x = \frac{1}{6} \times x$

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

Multiply by on both sides.

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

x=18

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Example Question #25 : Two Step Equations With Fractions

Solve:

$\frac{2}{7}x -3 = \frac{22}{7}$

Possible Answers:

$\frac{43}{2}$

$\frac{21}{2}$

$-\frac{21}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{43}{2}$

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 solve for the unknown variable, first add three on both sides.

$\frac{2}{7}x -3 +3= \frac{22}{7}+3$

$\frac{2}{7}x= \frac{22}{7}+\frac{21}{7}$

$\frac{2}{7}x= \frac{43}{7}$

Multiply $\frac{7}{2}$ on both sides.

$\frac{2}{7}x \times \frac{7}{2}= \frac{43}{7}\times \frac{7}{2}$

The seven in the numerator and in the denominator cancel out and we are left with the final solution,

$x=\frac{43}{2}$ .

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Example Question #81 : Two Step Equations

Solve: $\frac{7}{12}x +9 = 12$

Possible Answers:

$-\frac{7}{2}$

$\frac{36}{7}$

$-\frac{9}{7}$

$-\frac{8}{7}$

Correct answer:

$\frac{36}{7}$

Explanation:

Subtract nine from both sides of the equation.

$\frac{7}{12}x +9 -9= 12-9$

$\frac{7}{12}x = 12-9$

$\frac{7}{12}x = 3$

Multiply $\frac{12}{7}$ on both sides of the equation to isolate the unknown variable.

$\frac{7}{12}x \times \frac{12}{7} = 3\times \frac{12}{7}$

$x=\frac{36}{7}$

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Example Question #22 : Two Step Equations With Fractions

Solve: $\frac{1}{2}x -\frac{7}{8} = \frac{15}{8}$

Possible Answers:

$\frac{11}{16 }$

$\frac{16 }{11}$

$\frac{2}{11}$

$\frac{11}{2}$

Correct answer:

$\frac{11}{2}$

Explanation:

In order to solve for the unknown variable, add $\frac{7}{8}$ on both sides of the equation.

$\frac{1}{2}x -\frac{7}{8} +\frac{7}{8}= \frac{15}{8}+\frac{7}{8}$

Simplify both sides of the equation. The denominators are like, which means we do not need to find a lowest common denominator.

$\frac{1}{2}x = \frac{15}{8}+\frac{7}{8}$

Add the numerators on the right side. The denominators will remain the same.

$\frac{1}{2}x = \frac{22}{8}$

Multiply by the reciprocal of $\frac{1}{2}$ , or , on both sides to eliminate the fraction on the left side of the equation.

$\frac{1}{2}x \times2= \frac{22}{8}\times2$

Simplify both sides of the equation.

$x=\frac{44}{8}$

This fraction can still be reduced. Expand by their common factors.

$x=\frac{44}{8} = \frac{11 \times 4}{2 \times 4} = \frac{11}{2}$

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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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Pre-Algebra : Two-Step Equations with Fractions

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #21 : Two Step Equations With Fractions

Example Question #81 : Two Step Equations

Example Question #21 : Two Step Equations With Fractions

Example Question #141 : Algebraic Equations

Example Question #24 : Two Step Equations With Fractions

Example Question #25 : Two Step Equations With Fractions

Example Question #81 : Two Step Equations

Example Question #22 : Two Step Equations With Fractions

Example Question #28 : Two Step Equations With Fractions

Example Question #24 : Two Step Equations With Fractions

All Pre-Algebra Resources

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