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Pre-Algebra : Two-Step Equations with Fractions

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Example Questions

Example Question #11 : Two Step Equations With Fractions

Solve for x: $\frac{3}{2}x+\frac{1}{8}=10$

Possible Answers:

$5 \frac{5}{6}$

$9 \frac{7}{12}$

$6 \frac{7}{12}$

$6\frac{5}{8}$

$5 \frac{1}{4}$

Correct answer:

$6 \frac{7}{12}$

Explanation:

To solve, use inverse opperations: do the opposite steps in the opposite order. Order of opperations is usually PEMDAS, with addition and subtraction last, so we'll do addition/subtraction first:

$\frac{3}{2}x+\frac{1}{8}=10$ since it says to add $\frac{1}{8}$ , we will do the opposite and subtract $\frac{1}{8}$ from both sides:

$\frac{3}{2}x=9 \frac{7}{8}$ Next we will address multiplication/division. Right now we are multiplying times the fraction $\frac{3}{2}$ . Now we want to multiply both sides times its opposite, the reciprocal $\frac{2}{3}$ :

$x= \frac{2}{3}*(9 \frac{7}{8})$ The easiest way to do this is to think of the mixed number $9 \frac{7}{8}$ as the addition $9+ \frac{7}{8}$ and multiply each part times $\frac{2}{3}$ :

$\frac{9}{1}* \frac{2}{3}= 6; \frac{7}{8}* \frac{2}{3} = \frac{7}{12}$

So our answer is $x=6 \frac{7}{12}$

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Example Question #12 : Two Step Equations With Fractions

Solve for

$\frac{1}{8}\ X - 10 = 6$

Possible Answers:

128

116

Correct answer:

128

Explanation:

$\frac{1}{8} X - 10 = 6$

Add to each side

$\frac{1}{8}\ X = 16$

Divide both sides by $\frac{1}{8}$ , or multiply by the reciprocal which is $\frac{8}{1}$

X = 128

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Example Question #13 : Two Step Equations With Fractions

Solve the following equation for x.

$\frac{3}{4}x+\frac{2}{3}=\frac{1}{6}x-\frac{5}{12}$

Possible Answers:

$-\frac{7}{2}$

$-\frac{13}{7}$

$\frac{91}{144}$

$\frac{7}{15}$

Correct answer:

$-\frac{13}{7}$

Explanation:

To solve equations with fractions, follow the same method as with integers. Collect all the terms with the variable on one side and the terms without variables on the other.

$\frac{3}{4}x-\frac{1}{6}x=-\frac{5}{12}-\frac{2}{3}$

In order to combine the like terms (variables vs. non-variables), the denominators of the fractions must be the same.

$\frac{9}{12}x-\frac{2}{12}x=-\frac{5}{12}-\frac{2}{3}$

$\frac{7}{12}x=-\frac{13}{12}$

$x=-\frac{13}{7}$

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Example Question #11 : Two Step Equations With Fractions

Solve this equation: $6x-\frac{5}{2}=\frac{7}{2}$

Possible Answers:

No solution

x=2

The answer is not here.

x=3

x=-1

Correct answer:

The answer is not here.

Explanation:

$6x-\frac{5}{2}=\frac{7}{2}$

Move all fractions to one side:

$6x=\frac{7}{2}+\frac{5}{2}$

Simplify:

6x=6

x=1

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Example Question #12 : Two Step Equations With Fractions

Solve the two-step equation. Find the value of .

$\frac{x}{4} + 222 = 628$

Possible Answers:

x = 2278

x = 212.5

x = 2726

x = 101.5

x = 1624

Correct answer:

x = 1624

Explanation:

x / 4 + 222 = 628

- 222 - 222

x / 4 = 406

*4 *4

x = 1624

Check your answer by substituting 1624 back in for x and solving the problem. This time both sides of the equation should match.

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Example Question #16 : Two Step Equations With Fractions

Solve for :

$\frac{1}{8}x - 14 = 12$

Possible Answers:

208

118

3.25

Correct answer:

208

Explanation:

To solve for the variable, we will need to isolate the variable on one side of the equation and all other contstants on the other side. To do this, apply the opposite operation to manipulate the equation.

First, add to both sides:

$\frac{1}{8}x - 14 = 12$

$\frac{1}{8}x = 26$

Next, multiply both sides by to solve for :

x = 208

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Example Question #12 : Two Step Equations With Fractions

Solve for :

$\frac{23}{3y} = 3$

Possible Answers:

$\frac{9}{23}$

$\frac{23}{9}$

Correct answer:

$\frac{23}{9}$

Explanation:

First, multiply both sides by :

$\frac{23}{3y} = 3$

23 = 9y

Next, divide both sides by to solve for :

$y = \frac{23}{9}$

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Example Question #18 : Two Step Equations With Fractions

Solve for :

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

Possible Answers:

None of the other answers.

$x=\frac{23}{6}$

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

$x=\frac{6}{23}$

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

Correct answer:

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

Explanation:

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

Start by isolating the fraction attached the x variable:

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

The red terms cancel out.

We add the right side as usual.

$\frac{2}{3}x=\frac{9}{3}$

Reduce fractions where able and multiply by the reciprocal to isolate x:

${\color{Red} \frac{3}{2}*\frac{2}{3}}x=\frac{9}{3}*\frac{3}{2}$

The red terms cancel to 1 and the right is multiplied as usual.

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

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Example Question #13 : Two Step Equations With Fractions

Solve: $\frac{2}{3}x + 6=\frac{1}{6}$

Possible Answers:

$-\frac{35}{4}$

$-\frac{23}{36}$

$\frac{23}{36}$

$\frac{35}{4}$

$-\frac{5}{12}$

Correct answer:

$-\frac{35}{4}$

Explanation:

Subtract six from both sides of the equation.

$\frac{2}{3}x + 6-(6)=\frac{1}{6}-(6)$

$\frac{2}{3}x=\frac{1}{6}-\frac{36}{6}$

$\frac{2}{3}x=-\frac{35}{6}$

Multiply by $\frac{3}{2}$ on both sides.

$\frac{2}{3}x\times \frac{3}{2}=-\frac{35}{6}\times \frac{3}{2}$

$x=-\frac{35}{4}$

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Example Question #11 : Two Step Equations With Fractions

Solve: $\frac{1}{2}x-\frac{3}{2} = \frac{5}{2}$

Possible Answers:

$\frac{1}{8}$

$-\frac{1}{8}$

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 unknown variable, first add three halves on both sides of the equation.

$\frac{1}{2}x-\frac{3}{2}+\left(\frac{3}{2}\right) = \frac{5}{2}+\left(\frac{3}{2}\right)$

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

Multiply by two on both sides to eliminate the fraction coefficient in front of the variable.

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

x=8

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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 #11 : Two Step Equations With Fractions

Example Question #12 : Two Step Equations With Fractions

Example Question #13 : Two Step Equations With Fractions

Example Question #11 : Two Step Equations With Fractions

Example Question #12 : Two Step Equations With Fractions

Example Question #16 : Two Step Equations With Fractions

Example Question #12 : Two Step Equations With Fractions

Example Question #18 : Two Step Equations With Fractions

Example Question #13 : Two Step Equations With Fractions

Example Question #11 : Two Step Equations With Fractions

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