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Pre-Algebra : One-Step Equations with Decimals

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #171 : One Step Equations

Solve: 0.6x = 7

Possible Answers:

$\frac{5}{7}$

$\frac{5}{21}$

$\frac{35}{3}$

$\frac{12}{35}$

$\frac{1}{7}$

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 #172 : One Step Equations

Solve the following equation: 0.25x =8

Possible Answers:

$\frac{1}{32}$

8.25

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 #171 : One Step Equations

Solve for a in the following equation:

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

Possible Answers:

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

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

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

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

a = 1

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 #361 : Algebraic Equations

Solve for :

0.95x=285

Possible Answers:

284.05

295.95

290

300

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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Example Question #181 : One Step Equations

Simplify the following equation:

x-.49=.51

Possible Answers:

x=.05

x=0

x=1

x=-.02

x=.02

Correct answer:

x=1

Explanation:

This is a one-step problem where you need to isolate x by moving the to the other side by addition.

So:

x=.49+.51 when you simplify this you get a final answer of x=1

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Example Question #362 : Algebraic Equations

Find the value of x.

x - 3.45 = 7.20

Possible Answers:

x = 9.20

x = 10.45

x = -3.75

x = 3.45

x = 10.65

Correct answer:

x = 10.65

Explanation:

In order to solve this problem simply add 3.45 on both sides to isolate the variable . Once added on both sides the should be isolated and the value on the right is 3.45 + 7.20

x - 3.45 = 7.20

x - 3.45 + 3.45 = 7.20 + 3.45 (Adding 3.45 on both sides)

x - 0 = 10.65

Therefore,

x = 10.65

If you need to check your answer simply plug in your answer into the variable to see if your solution is correct:

10.65 - 3.45 = 7.20 It works!

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Example Question #64 : One Step Equations With Decimals

Solve for y

10.34 - y = 6.01

Possible Answers:

y = 4.33

y = 4.30

y = 4.31

y = 4

y = 4.32

Correct answer:

y = 4.33

Explanation:

In this problem we must isloate the variable to one side. The best strategy to solve this problem is to bring the to the right side of the equation because it currently has a negative sign on the left side. So we will do as follows:

10.34 - y + y = 6.01 + y

10.34 + 0 = 6.01 + y

10.34 = 6.01 + y

We then subtract 6.01 from both sides so we can isolate .

10.34 - 6.01 = 6.01 - 6.01 +y

4.33 = 0 + y

y = 4.33

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Pre-Algebra : One-Step Equations with Decimals

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #171 : One Step Equations

Example Question #172 : One Step Equations

Example Question #171 : One Step Equations

Example Question #62 : One Step Equations With Decimals

Example Question #171 : One Step Equations

Example Question #171 : One Step Equations

Example Question #361 : Algebraic Equations

Example Question #181 : One Step Equations

Example Question #362 : Algebraic Equations

Example Question #64 : One Step Equations With Decimals

All Pre-Algebra Resources

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