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Pre-Algebra : Algebraic Equations

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Example Question #351 :Algebraic Equations

Solve: 0.6x = 24

Possible Answers:

$\frac{1}{4}$

400

0.04

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, divide both sides by 0.6

$\frac{0.6x }{0.6}= \frac{24}{0.6}$

Decimals may be written as fractions.

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

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

Substitute and solve.

$x=\frac{24}{1}\times\frac{10}{6}$

$x=\frac{240}{6}=\frac{6\cdot 40}{6}$

The six in the numerator and in the denominator cancel out and we are left with the final answer,

x=40 .

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Example Question #352 :Algebraic Equations

Solve: 0.123+x = 456

Possible Answers:

333

3.33

0.455877

0.333

455.877

Correct answer:

455.877

Explanation:

In order to solve for, subtract 0.123 from both sides.

0.123+x -0.123= 456-0.123

x=455.877

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Example Question #353 :Algebraic Equations

Evaluate:

0.09x = 27

Possible Answers:

300

3000

26.91

27.09

Correct answer:

300

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.

Solve by dividing 0.09 on both sides of the equation. Move the decimal two places to the right.

$\frac{0.09x}{0.09} = \frac{27}{0.09} =\frac{2700}{9}$

Now factor the numerator to find values that can cancel out.

$\frac{2700}{9}=\frac{9\cdot 300}{9}$

The nine in the numerator and denominator reduce to one and we are left with our final answer,

x=300 .

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Example Question #354 :Algebraic Equations

Solve: 0.39x = 7.8

Possible Answers:

0.741

7.41

200

Correct answer:

Explanation:

Divide 0.39 on both sides of the equation.

$\frac{0.39x}{0.39} = \frac{7.8}{0.39}$

x=20

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Example Question #355 :Algebraic Equations

Solve:

2.02x= -0.202

Possible Answers:

-0.01

0.1

-0.1

Correct answer:

-0.1

Explanation:

Divide by 2.02 on both sides of the equation.

$\frac{2.02x}{2.02}=\frac{ -0.202}{2.02}$

Decimals may be written as fractions.

$-0.202=-\frac{202}{1000}; 2.02=\frac{202}{100}$

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

Substitute and solve.

$x=-\frac{202}{1000}\times\frac{100}{202}$

x=-0.1

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Example Question #356 :Algebraic Equations

Solve: x-0.56 = 1.4

Possible Answers:

1.52

1.16

1.96

0.69

1.6

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 #357 :Algebraic Equations

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 #358 :Algebraic Equations

Solve: 2x = 0.003

Possible Answers:

0.015

0.15

0.0015

0.006

0.06

Correct answer:

0.0015

Explanation:

Solve by dividing both sides by 2.

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

等式的右边部分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 #359 :Algebraic Equations

Solve: 0.6x = 7

Possible Answers:

$\frac{5}{7}$

$\frac{35}{3}$

$\frac{1}{7}$

$\frac{5}{21}$

$\frac{12}{35}$

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 相当于 $\frac{3}{5}$ .

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

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 #360 :Algebraic 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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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #351 :Algebraic Equations

Example Question #352 :Algebraic Equations

Example Question #353 :Algebraic Equations

Example Question #354 :Algebraic Equations

Example Question #355 :Algebraic Equations

Example Question #356 :Algebraic Equations

Example Question #357 :Algebraic Equations

Example Question #358 :Algebraic Equations

Example Question #359 :Algebraic Equations

Example Question #360 :Algebraic Equations

All Pre-Algebra Resources

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