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Pre-Algebra : One-Step Equations

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Example Questions

Example Question #44 : One Step Equations With Fractions

Solve for a in the following equation:

$\frac{2}{3} + a = \frac{1}{2}$

Possible Answers:

$a = \frac{7}{6}$

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

$a = -\frac{1}{6}$

$a = \frac{3}{5}$

$a = \frac{1}{6}$

Correct answer:

$a = -\frac{1}{6}$

Explanation:

When solving for a, we want to get a by itself. So in the equation,

$\frac{2}{3} + a = \frac{1}{2}$

we must subtract $\frac{2}{3}$ from both sides. We get

$\frac{2}{3} + a - \frac{2}{3} = \frac{1}{2} - \frac{2}{3}$

$a = \frac{1}{2} - \frac{2}{3}$

When subtracting fractions, we need to find a common denominator. In this case, it's 6. So,

$a = \frac{3}{6} - \frac{4}{6}$

Now, we subtract the numerators and get

$a = - \frac{1}{6}$

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Example Question #51 : One Step Equations With Fractions

Solve the following equation:

$\frac{1}{5}x=\frac{3}{5}$

Possible Answers:

$x=\frac{3}{25}$

x=15

x=3

$x=\frac{8}{5}$

None of the above.

Correct answer:

x=3

Explanation:

This is a one-step problem in which you need to multiply both sides by to isolate "x."

You will then get:

$x=\frac{3}{5}*5$

The fives cancel and you are left with:

x=3

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

Solve for .

$p-\frac{2}{5}=3$

Possible Answers:

p=4

p=3

$p=\frac{13}{5}$

$p=\frac{17}{5}$

Correct answer:

$p=\frac{17}{5}$

Explanation:

Perform the same operation on both sides of the equation.

$p-\frac{2}{5}=3$

It will be easier to write the right side of the equation as a fraction.

$3=\frac{15}{5}$

$p-\frac{2}{5}=\frac{15}{5}$

Now, we add two-fifths to both sides of the equation.

$p-\frac{2}{5}+\frac{2}{5}=\frac{15}{5}+\frac{2}{5}$

$p=\frac{17}{5}$

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Example Question #1 : One Step Equations With Decimals

Solve for :

0.75x=9

Possible Answers:

9.75

Correct answer:

Explanation:

The goal is to isolate the variable on one side.

0.75x=9

Divide each side by 0.75 :

$\frac{0.75x}{0.75}=\frac{9}{0.75 }$

x=12

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Example Question #2 : One Step Equations With Decimals

Solve for :

9.25x=74

Possible Answers:

Correct answer:

Explanation:

The goal is to isolate the variable on one side.

9.25x=74

Divide each side by 9.25 :

$\frac{9.25x}{9.25}=\frac{74}{9.25}$

x=8

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Example Question #3 : One Step Equations With Decimals

Solve for :
1.05+n=3.72

Possible Answers:

n=2.67

n=4.77

n=3.91

n=3.54

Correct answer:

n=2.67

Explanation:

1.05+n=3.72

1.05+n-1.05=3.72-1.05

n=2.67

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Example Question #3 : One Step Equations With Decimals

Solve for :

1.75+x=4.2

Possible Answers:

x=2.45

x=5.95

x=7.35

x=2.4

Correct answer:

x=2.45

Explanation:

1.75+x=4.2

Subtract 1.75 from both sides of the equation:

1.75+x-1.75=4.2-1.75

x=2.45

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Example Question #5 : One Step Equations With Decimals

Solve for :

$\small .6x=6$

Possible Answers:

$\small 8$

$\small 3.6$

$\small 10$

$\small 1$

$\small 36$

Correct answer:

$\small 10$

Explanation:

To isolate , we must divide both sides by .6:

$\small \small \frac{.6x}{.6}=\frac{6}{.6}$

$\small 1x=10$

$\small x=10$

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Example Question #4 : One Step Equations With Decimals

Solve for :

$\frac{x}{0.15} = 3$

Possible Answers:

0.30

0.15

3.45

0.45

Correct answer:

0.45

Explanation:

The goal is to isolate the variable on one side.

$\frac{x}{0.15} = 3$

The opposite operation of division is multiplication, therefore , multiply each side by 0.15:

$\frac{0.15x}{0.15} = 0.15\times 3$

The left hand side can be reduced by recalling that anything divided by itself is equal to 1:

$1\times x = 0.15 \times 3$

The identity law of multiplication takes effect and we get the solution as:

x = 0.45

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Example Question #4 : One Step Equations With Decimals

Solve for :

x - 0.23 = 7.12

Possible Answers:

30.96

8.35

7.35

6.89

7.36

Correct answer:

7.35

Explanation:

The goal is to isolate the variable on one side.

x - 0.23 = 7.12

The opposite operation of subtraction is addition so add 0.23 to each side:

x - 0.23 + 0.23 = 7.12 + 0.23

Simplifying, we get the final solution:

x = 7.35

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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 #44 : One Step Equations With Fractions

Example Question #51 : One Step Equations With Fractions

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

Example Question #1 : One Step Equations With Decimals

Example Question #2 : One Step Equations With Decimals

Example Question #3 : One Step Equations With Decimals

Example Question #3 : One Step Equations With Decimals

Example Question #5 : One Step Equations With Decimals

Example Question #4 : One Step Equations With Decimals

Example Question #4 : One Step Equations With Decimals

All Pre-Algebra Resources

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