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Pre-Algebra : One-Step Equations

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Example Questions

Example Question #58 : One Step Equations With Decimals

Solve: x-0.56 = 1.4

Possible Answers:

1.6

1.16

1.96

1.52

0.69

Correct answer:

1.96

Explanation:

Add 0.56 on both sides of the equation.

x-0.56 +0.56= 1.4+0.56

x= 1.40+0.56

x= 1.96

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Example Question #59 : One Step Equations With Decimals

Solve: 0.6x = 36

Possible Answers:

216

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, divide both sides by 0.6 .

$\frac{0.6x}{0.6} = \frac{36}{0.6}$

Decimals may be written as fractions.

$0.6=\frac{6}{10}$

Dividing by a fraction is the same as multiplying by its reciprocal:

$\frac{36}{1}\times \frac{10}{6}=\frac{360}{6}$

Now factor the numerator to find like terms that can reduce.

$\frac{360}{6}=\frac{60\cdot 6}{6}$

The six in the numerator and denominator reduce to one and the final solution becomes,

x=60 .

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Example Question #352 : Algebraic Equations

Solve: 2x = 0.003

Possible Answers:

0.15

0.0015

0.06

0.015

0.006

Correct answer:

0.0015

Explanation:

Solve by dividing both sides by 2.

$\frac{2x}{2} = \frac{0.003}{2}$

The fraction on the right side of the equation can be rewritten as:

$x= \frac{0.003}{2} = \frac{\frac{3}{1000}}{2}$

Dividing by two is also similar to multiplying by one half.

$x= \frac{3}{1000} \times \frac{1}{2}= \frac{3}{2000}$

x=0.0015

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Example Question #61 : One Step Equations With Decimals

Solve: 0.6x = 7

Possible Answers:

$\frac{12}{35}$

$\frac{5}{7}$

$\frac{35}{3}$

$\frac{5}{21}$

$\frac{1}{7}$

Correct answer:

$\frac{35}{3}$

Explanation:

In order to solve for the unknown variable, we must convert the decimal in front of the variable to a fraction. The decimal 0.6 is equivalent to $\frac{3}{5}$ .

$\frac{3}{5}x = 7$

Our goal is to get a coefficient of one in front of the . Multiply the reciprocal of $\frac{3}{5}$ on both sides of the equation.

$\frac{3}{5}x \times \frac{5}{3}= 7\times \frac{5}{3}$

The fractions will cancel on the left side of the equation. Multiply the seven with the numerator of the fraction on the right side.

$x=\frac{35}{3}$

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Example Question #62 : One Step Equations With Decimals

Solve the following equation: 0.25x =8

Possible Answers:

8.25

$\frac{1}{32}$

7.75

Correct answer:

Explanation:

Convert the coefficient in front of the variable to a fraction.

$0.25 =\frac{1}{4}$

Rewrite the equation.

$\frac{1}{4}x=8$

In order to isolate the variable, we need to multiply four on both sides of the equation to eliminate the fraction.

$\frac{1}{4}x \times 4=8\times 4$

The answer is: x=32

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Example Question #171 : One Step Equations

Solve for :

x-7.71=-2.19

Possible Answers:

9.9

9.09

-9.9

5.52

-5.52

Correct answer:

5.52

Explanation:

To solve this problem, the variable (in this case ) must be isolated to one side.

Because 7.71 is subtracted on the side with the variable, we must add 7.71 to both sides:

x-7.71=-2.19

x-7.71+7.71=-2.19+7.71

x=-2.19+7.71

x=5.52

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Example Question #62 : One Step Equations With Decimals

Solve the one step equation below.

1.25x = 25

Possible Answers:

x = 15

x = 31.25

x = 26.25

x = 20

x = 23.75

Correct answer:

x = 20

Explanation:

Use properties of Equality to solve.

1.25x = 25

\ 1.25 \ 1.25

x = 20

Check your answer.

1.25 * 20 = 25

25 = 25

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Example Question #363 : Algebraic Equations

Solve for a in the following equation:

$a - \frac{3}{4} = \frac{1}{4}$

Possible Answers:

$a = \frac{2}{4}$

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

$a = \frac{1}{4}$

a = 1

$a = \frac{5}{4}$

Correct answer:

a = 1

Explanation:

When solving for a, we need to get a by itself. In the equation

$a - \frac{3}{4} = \frac{1}{4}$

we must add $\frac{3}{4}$ to both sides. We get

$a - \frac{3}{4} + \frac{3}{4} = \frac{1}{4} + \frac{3}{4}$

$a = \frac{1}{4} + \frac{3}{4}$

Now, we combine the fractions. Since they already have a common denominator, we add the numerators. we get

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

which is the same as

a = 1 .

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Example Question #171 : One Step Equations

Solve for in the following equation:

$\frac{x}{2.5} = 10$

Possible Answers:

x = 25

x = 7.5

x = 12.5

x = 250

x = 0.25

Correct answer:

x = 25

Explanation:

When solving for x, we multiply both sides by 2.5.

So,

$\frac{x}{2.5} = 10$

$\frac{x}{2.5} \cdot 2.5 = 10 \cdot 2.5$

x = 25

Note that even though there are decimals in the equation, you still solve it using the same methods.

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Example Question #66 : One Step Equations With Decimals

Solve for :

0.95x=285

Possible Answers:

290

284.05

300

295.95

270.75

Correct answer:

300

Explanation:

We must isolate , so we simply divide both sides of the equation by 0.95 , as follows:

0.95x=285

$\frac{0.95x}{0.95}=\frac{285}{0.95}$

x=300

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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 #58 : One Step Equations With Decimals

Example Question #59 : One Step Equations With Decimals

Example Question #352 : Algebraic Equations

Example Question #61 : One Step Equations With Decimals

Example Question #62 : One Step Equations With Decimals

Example Question #171 : One Step Equations

Example Question #62 : One Step Equations With Decimals

Example Question #363 : Algebraic Equations

Example Question #171 : One Step Equations

Example Question #66 : One Step Equations With Decimals

All Pre-Algebra Resources

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