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Pre-Algebra : Algebraic Equations

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Example Questions

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 #61 : One Step Equations With Decimals

Solve for :

0.95x=285

Possible Answers:

300

290

295.95

270.75

284.05

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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Example Question #71 : One Step Equations With Decimals

Solve.

$10.8\times 22.3= ?$

Possible Answers:

240.74

249.74

260.84

240.84

Correct answer:

240.84

Explanation:

10.8
22.3
324
2160
21600

240.84

Multiply the numbers as you would any three-digit numbers, ignoring the decimal points. After adding the three lines together, place the decimal point however many spots from the right as there are decimal points moved from the right in the original equation. Because both 10.8 and 22.3 have decimals one over from the right of the number, totaling two decimals over, you will move the decimal over two decimal places in the final solution.

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Example Question #361 : Algebraic Equations

Solve for :

$\frac{x}{0.5} = 2$

Possible Answers:

0.25

0.5

Correct answer:

Explanation:

The goal is to isolate the variable on one side.

$\frac{x}{0.5} = 2$

The opposite operation of division is multiplication, therefore , multiply each side by 0.5:

$\frac{0.5x}{0.5} = 0.5\times 2$

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

$1\times x = 0.5 \times 2$

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

x = 1

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

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 #61 : One Step Equations With Decimals

Example Question #181 : One Step Equations

Example Question #362 : Algebraic Equations

Example Question #64 : One Step Equations With Decimals

Example Question #71 : One Step Equations With Decimals

Example Question #361 : Algebraic Equations

All Pre-Algebra Resources

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