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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #181 : Algebraic Equations

Solve: 0.2x-0.4 = 0.6

Possible Answers:

1.1

Correct answer:

Explanation:

In order to solve this equation, first add 0.4 on both sides of the equation.

0.2x-0.4 +0.4= 0.6+0.4

Simplify the left and right side of the equation.

0.2x=1

Convert the decimal on the left side of the equation to a fraction.

$0.2 = \frac{1}{5}$

Rewrite the equation.

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

To isolate the unknown variable, multiply by the reciprocal of $\frac{1}{5}$ , or , on each side of the equation.

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

Simplify the left and the right side of the equation.

x=5

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Example Question #123 : Two Step Equations

Solve: 0.75x +1= -0.25x

Possible Answers:

$\frac{5}{4}$

$-\frac{1}{2}$

$\frac{4}{5}$

Correct answer:

Explanation:

In order to solve this equation, we need to group the terms and separate the integer .

Add 0.25x on both sides.

0.75x +0.25x -1=0

Add both sides by .

0.75x +0.25x -1+1=0+1

Add the left side of the equation to get .

The answer is: x= -1

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Example Question #124 : Two Step Equations

Solve the following equation: 9+0.9x = 19

Possible Answers:

$\frac{9}{100}$

$\frac{1}{90}$

$\frac{100}{9}$

Correct answer:

$\frac{100}{9}$

Explanation:

To isolate the variable, subtract nine from both sides of the equation.

9+0.9x -9= 19-9

Simplify both sides of the equation.

0.9x = 10

Convert the decimal on the left side of the equation to a fraction.

$0.9 = \frac{9}{10}$

Rewrite the equation.

$\frac{9}{10}x= 10$

Multiply both sides by $\frac{10}{9}$ to get by itself.

$\frac{9}{10}x \times \frac{10}{9}= 10 \times \frac{10}{9}$

Simplify both sides of the equation. Multiply the tens together on the right side of the equation and leave the fraction in improper form.

The answer is: $x= \frac{100}{9}$

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Example Question #125 : Two Step Equations

Solve the two-step equation below.

32x -8 = 224

Possible Answers:

x = 7424

x = 7.25

x = 6.75

x = 200

x = 8

Correct answer:

x = 7.25

Explanation:

Use properties of equality. Start with either subtraction or addition then multiplication or division.

32x -8 = 224

+ 8 + 8

32x = 232

Now divide by 32.

$\frac{32x}{32} = \frac{232}{32}$

x = 7.25

Check your answer by substituting 7.25 in place of x.

(32 * 7.25) - 8 = 224

232 - 8 = 224

224 = 224

Both sides are equal.

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Example Question #126 : Two Step Equations

Find the solution for y.

1.25y-3.4=6.6

Possible Answers:

y=8

y=8.25

y=4

y=3.3

y=9

Correct answer:

y=8

Explanation:

In this two step equation we must isolate and find the solution of y. So the first step is to add both sides by 3.4 as follows:

1.25y - 3.4 +3.4 = 6.6 + 3.4

1.25y +0 = 10.0

1.25y=10.0

The next step is divide both sides by 1.25 as follows:

$\frac{1.25}{1.25}y=\frac{10.0}{1.25}\Rightarrow y =\frac{10.0}{1.25}=8$

You can check your answer by inserting 8 into y in the original equation as follows:

$1.25(8)-3.4=6.6\Rightarrow 10.0-3.4=6.6\Rightarrow 6.6=6.6$

It's correct!

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Example Question #1 : One Step Equations With Integers

Solve for :

x+7=2

Possible Answers:

Correct answer:

Explanation:

Isolate the variable to one side.

Subtract from both sides:

x+7=2

x+7-7=2-7

x=-5

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Example Question #2 : One Step Equations With Integers

Solve for :

3x=27

Possible Answers:

Correct answer:

Explanation:

We need to isolate by dividing by 3.

Remember, what you do on one side, you must do on the other side.

Since you divided by , you also have to divde by :

$\frac{3x}{3}= \frac{27}{3}$

x=9

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Example Question #2 : One Step Equations

Solve for $\small x$ :

x+1=0

Possible Answers:

$\small -1$

$\small 1$

Correct answer:

$\small -1$

Explanation:

To solve this you must isolate your $\small x$ by subtracting 1 from both sides to get

x=0-1 or x=-1

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Example Question #3 : One Step Equations With Integers

Solve for x:

x + 4 = -12

Possible Answers:

x= -16

x= 4

x= -48

x= -8

x= -3

Correct answer:

x= -16

Explanation:

Step 1: isolate x

x+4-4=-12-4

x=-12-4

Step 2: solve

x=-16

If it's helpful, when you subtract a positive integer from a negative integer, you can think of it in terms of absolute value:

$-12-4=-\left | 12+4\right |=-\left | 16\right |=-16$

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Example Question #3 : One Step Equations

Solve for $\small x$ :

$\small 8x = 64$

Possible Answers:

Correct answer:

Explanation:

To solve this equation, isolate $\small x$ by dividing both sides of the equation by 8:

$\small 8x=64$

$\small \frac{8x}{8}= \frac{64}{8}$

$\small x=8$

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #181 : Algebraic Equations

Example Question #123 : Two Step Equations

Example Question #124 : Two Step Equations

Example Question #125 : Two Step Equations

Example Question #126 : Two Step Equations

Example Question #1 : One Step Equations With Integers

Example Question #2 : One Step Equations With Integers

Example Question #2 : One Step Equations

Example Question #3 : One Step Equations With Integers

Example Question #3 : One Step Equations

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