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High School Math : How to solve two-step equations with fractions in pre-algebra

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Example Questions

Example Question #1 : How To Solve Two Step Equations With Fractions In Pre Algebra

Solve for :

$\frac{12}{x} + 9 = 13$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{4}$

Correct answer:

Explanation:

This equation can be solved in three steps.

First, subtract from both sides of the equation to isolate the variable and its coefficient on the left side of the equation.

$\frac{12}{x} + 9 = 13$

$\rightarrow (\frac{12}{x} + 9) - 9 = (13) - 9$

$\rightarrow \frac{12}{x} = 4$

Now multiply both sides by since cannot be solved for while it is in the denominator.

$(\frac{12}{x}) \times x = (4) \times x$

$\rightarrow 12 = 4x$

Finally, divide both sides by to isolate and find the solution.

$\frac{(12)}{4} = \frac{(4x)}{4}$

$\rightarrow 3 = x$

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Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Solve for $\small a$ .

$\frac{12}{a}-7=-1$

Possible Answers:

a=2

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

a=3

a=1

Correct answer:

a=2

Explanation:

$\frac{12}{a}-7=-1$

Add 7 to both sides.

$\frac{12}{a}-7+7=-1+7$

$\frac{12}{a}=6$

Multiply both sides by $\small a$ .

$\frac{12}{a}(a)=6a$

12=6a

Divide both sides by 6.

$\frac{12}{6}=\frac{6a}{6}$

2=a

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Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Solve for $\small x$ .

$(2x\div4) +5 = 25$

Possible Answers:

x=0

x=25

x=20

x=2/6

x=40

Correct answer:

x=40

Explanation:

$(2x\div4) +5 = 25$

We need to isolate $\small x$ . First, subtract $\small 5$ from both sides.

$(2x\div4) +5-5 = 25-5$

$(2x\div4) = 20$

Multiply both sides by $\small 4$ .

$2x\div4 *4= 20*4$

2x=80

Finally, divide both sides by $\small 2$ .

$\frac{2x}{2}=\frac{80}{2}$

x=40

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Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Solve for the value of $\small a$ .

$\frac{a}{4}+3=12$

Possible Answers:

$a=\frac{15}{4}$

a=36

a=60

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

Correct answer:

a=36

Explanation:

$\frac{a}{4}+3=12$

We need to work to isolate the variable using inverse functions.

Subtract $\small 3$ from both sides.
$\frac{a}{4}+3-3=12-3$

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

Multiply both sides by $\small 4$ .

$(4)\frac{a}{4}=(4)(9)$

a=36

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Example Question #3 : How To Solve Two Step Equations With Fractions In Pre Algebra

$x=\frac{2}{3}*18$

Solve for .

Possible Answers:

Correct answer:

Explanation:

$x=\frac{2}{3}*18$

From here, you can either plug this into your calculator, or take the equation in pieces:

$x=\frac{2*18}{3}$

$x=\frac{36}{3}$

x=12

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Example Question #3 : How To Solve Two Step Equations With Fractions In Pre Algebra

$\frac{2}{3}*(x+5)=12$

Solve for .

Possible Answers:

$10\tfrac{1}2{}$

Correct answer:

Explanation:

To solve $\frac{2}{3}*(x+5)=12$ , first we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by a reciprocal, so multiply both sides by $\frac{3}{2}$ .

$\frac{2}{3}*(x+5)=12$

$\frac{3}{2}*\frac{2}{3}*(x+5)=12*\frac{3}{2}$

$x+5=12*\frac{3}{2}$

$x+5=\frac{12*3}{2}$

$x+5=\frac{36}{2}$

x+5=18

Subtract from both sides.

x+5-5=18-5

x=18-5

x=13

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Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

$\frac{2}{3}x=10$

Solve for .

Possible Answers:

$\frac{3}{20}$

$\frac{20}{3}$

Correct answer:

Explanation:

To solve $\frac{2}{3}x=10$ , we need to get rid of the fraction. To do that, we multiply both sides by the reciprocal of that fraction.

$\frac{3}{2}*\frac{2}{3}x=10*\frac{3}{2}$

$x=10*\frac{3}{2}$

From here, you can either plug that fraction into your calculator or solve in pieces.

$x=\frac{10*3}{2}$

$x=\frac{30}{2}$

x=15

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Example Question #8 : How To Solve Two Step Equations With Fractions In Pre Algebra

$\frac{3}{4}x=118+2$

Solve for .

Possible Answers:

480

$88\tfrac{1}{2}$

$157\tfrac{1}{3}$

160

Correct answer:

160

Explanation:

To solve for , we need to isolate our variable. That means that we want ONLY the on the left side of the equation.

First, combine our like terms on the right side.

$\frac{3}{4}x=118+2$

$\frac{3}{4}x=120$

Now divide both sides by $\frac{3}{4}$ . Remember, dividing by a fraction is the same as multiplying by the reciprocal, so we're going to multiply both sides by $\frac{4}{3}$ .

$\frac{3}{4}x*\frac{4}{3}=120*\frac{4}{3}$

Since $\frac{3}{4}*\frac{4}{3}=\frac{12}{12}=1$ , we can ignore it.

$x=\frac{120}{1}*\frac{4}{3}$

$x=\frac{480}{3}$

x=160

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Example Question #9 : How To Solve Two Step Equations With Fractions In Pre Algebra

A glass jar is filled to the top with 100 blue marbles, 75 red marbles, and 25 yellow marbles. Each time a marbles is picked from the jar, it must be returned to the jar before another marble is picked again. What is the probability of picking a red marble?

Possible Answers:

3/8

1/8

2/3

5/8

3/4

Correct answer:

3/8

Explanation:

First, find the total number of marbles in the glass jar: 100 + 75 + 25 = 200 marbles in total.

It is given that there are 75 red marbles, thus: 75/200 = 3/8 .

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Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

$15=\frac{Y}{3}-9$

Y=?

Possible Answers:

Correct answer:

Explanation:

First add 9 to both sides:

$15+(9)=\frac{Y}{3}-9+(9)$

$24=\frac{Y}{3}$

Then multiply both sides by 3:

$24\left ( 3\right )=\frac{Y}{3}\left ( 3\right )$

72=Y

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High School Math : How to solve two-step equations with fractions in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #3 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #3 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #8 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #9 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

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