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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #14 : Two Step Equations With Decimals

Find the value of in the equation.

6.75x + 12 = 93

Possible Answers:

x = 8

x = 12

x = 74.25

x = 15.5

x = 88.25

Correct answer:

x = 12

Explanation:

With a two step equation don't forget when solving the problem do the inverse operation. That means opposite of addition is subtraction and vice versa and opposite of multiplication is division and vice versa. Make sure what ever you do to one side you do to the other as well. Tip: Do addition or subtraction first, then multiplication or division.

6.75x + 12 = 93

${\color{Red} - 12 - 12}$

$\frac{6.75x}{{\color{Red}6.75 }} = \frac{81}{{\color{Red}6.75 }}$

x = 12

Check your answer by substituting x back into the equation. Both sides should equal.

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Example Question #12 : Two Step Equations With Decimals

Solve: 0.5x + 0.5 = -1.5

Possible Answers:

$-\frac{1}{2}$

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 unknown variable, first subtract 0.5 from both sides.

0.5x + 0.5-(0.5) = -1.5-(0.5)

0.5x =-2

Divide both sides by 0.5 .

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

x=-4

If dividing by a decimal if difficult, multiply the numerator and denominator by ten to get whole integers.

$\frac{-2\cdot 10}{0.5\cdot 10}=\frac{-20}{5}$

Now factor the numerator to find a common factor to cancel out.

$\frac{-20}{5}=\frac{-4\cdot 5}{5}=-4$

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Example Question #173 : Algebraic Equations

Solve: 0.25x +0.75 = 1

Possible Answers:

0.1

0.6

Correct answer:

Explanation:

To isolate the unknown variable, first subtract 0.75 from both sides.

0.25x +0.75 -0.75= 1-0.75

0.25x= 0.25

x=1

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Example Question #174 : Algebraic Equations

Solve: 0.5x + 0.05 = 1

Possible Answers:

1.9

Correct answer:

1.9

Explanation:

To solve for the unknown variable, first subtract 0.05 from both sides of the equation.

0.5x =0.95

Divide 0.5 on both sides.

$\frac{0.5x}{0.5} =\frac{0.95}{0.5}$

x=1.9

If dividing by decimals is difficult, just multiply both decimals by 100 to get integers.

$\frac{0.95\times 100}{0.5\times100} = \frac{95}{50}$

When you multiply by 100 you move the decimal two spaces to the right.

From here factor the numerator and cancel like terms.

$\frac{95}{50}=1.9$

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Example Question #16 : Two Step Equations With Decimals

Compute: 0.03x +0.3 = 0.03

Possible Answers:

$-\frac{1}{27}$

$-\frac{1}{10}$

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.

Subtract 0.3 from both sides of the equation.

0.03x +0.3 -0.3 = 0.03-0.3

0.03x =-0.27

Divide 0.03 on both sides.

x= -9

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Example Question #13 : Two Step Equations With Decimals

Solve:

0.2x-0.3x = 0.5

Possible Answers:

0.5

-0.5

-0.25

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 solve for , combine like-terms by subtracting.

-0.1x = 0.5

Divide both sides by -0.1 .

$\frac{-0.1x }{-0.1}= \frac{0.5}{-0.1}$

Decimals may be written as fractions.

$-0.1=-\frac{1}{10}$

$0.5=\frac{1}{2}$

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

Thus we can replace the decimals with their fraction equivalents:

$x=\frac{1}{2}\times -\frac{10}{1}=\frac{-10}{2}=\frac{-5\cdot 2}{2}$

Canceling out the two that is in the numerator and in the denominator we arrive at our final answer.

x= -5

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Example Question #18 : Two Step Equations With Decimals

Solve: 0.02+2x = 0.2

Possible Answers:

0.011

1.1

0.9

0.09

Correct answer:

0.09

Explanation:

Subtract 0.02 from both sides of the equation.

0.02+2x-0.02 = 0.2-0.02

2x=0.18

Divide by two on both sides.

$\frac{2x}{2}=\frac{0.18}{2}$

x=0.09

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Example Question #111 : Two Step Equations

Evaluate: 1.2x +0.12 = 12

Possible Answers:

9.9

8.9

0.09

0.99

0.1

Correct answer:

9.9

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.

Subtract 0.12 on both sides of the equation.

1.2x +0.12 -0.12 = 12-0.12

1.2x= 11.88

x=9.9

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Example Question #112 : Two Step Equations

Solve:

0.2^2+x = 1

Possible Answers:

0.8

0.6

0.06

0.96

0.45

Correct answer:

0.96

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.

First, square the decimal.

0.2^2 = 0.04

Subtract this value from both sides to isolate the unknown variable.

x = 1-0.04 = 0.96

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Example Question #171 : Algebraic Equations

Solve: -3x-1.5 = 4.5

Possible Answers:

Correct answer:

Explanation:

To solve for , first add 1.5 on both sides of the equation.

-3x-1.5 +1.5= 4.5+1.5

-3x=6

Divide both sides by negative three.

x=-2

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #14 : Two Step Equations With Decimals

Example Question #12 : Two Step Equations With Decimals

Example Question #173 : Algebraic Equations

Example Question #174 : Algebraic Equations

Example Question #16 : Two Step Equations With Decimals

Example Question #13 : Two Step Equations With Decimals

Example Question #18 : Two Step Equations With Decimals

Example Question #111 : Two Step Equations

Example Question #112 : Two Step Equations

Example Question #171 : Algebraic Equations

All Pre-Algebra Resources

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