Algebra Examples

$\frac{2020}{2021} (2 x - 3) - \frac{2019}{2020} (2 x - 3) = 0$

Step 1

Simplify $\frac{2020}{2021} \cdot (2 x - 3) - \frac{2019}{2020} \cdot (2 x - 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{2020}{2021} (2 x) + \frac{2020}{2021} \cdot - 3 - \frac{2019}{2020} \cdot (2 x - 3) = 0$

Step 1.1.2

Multiply $\frac{2020}{2021} (2 x)$ .

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Step 1.1.2.1

Combine $2$ and $\frac{2020}{2021}$ .

$\frac{2 \cdot 2020}{2021} x + \frac{2020}{2021} \cdot - 3 - \frac{2019}{2020} \cdot (2 x - 3) = 0$

Step 1.1.2.2

Multiply $2$ by $2020$ .

$\frac{4040}{2021} x + \frac{2020}{2021} \cdot - 3 - \frac{2019}{2020} \cdot (2 x - 3) = 0$

Step 1.1.2.3

Combine $\frac{4040}{2021}$ and $x$ .

$\frac{4040 x}{2021} + \frac{2020}{2021} \cdot - 3 - \frac{2019}{2020} \cdot (2 x - 3) = 0$

Step 1.1.3

Multiply $\frac{2020}{2021} \cdot - 3$ .

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Step 1.1.3.1

Combine $\frac{2020}{2021}$ and $- 3$ .

$\frac{4040 x}{2021} + \frac{2020 \cdot - 3}{2021} - \frac{2019}{2020} \cdot (2 x - 3) = 0$

Step 1.1.3.2

Multiply $2020$ by $- 3$ .

$\frac{4040 x}{2021} + \frac{- 6060}{2021} - \frac{2019}{2020} \cdot (2 x - 3) = 0$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{4040 x}{2021} - \frac{6060}{2021} - \frac{2019}{2020} \cdot (2 x - 3) = 0$

Step 1.1.5

Apply the distributive property.

$\frac{4040 x}{2021} - \frac{6060}{2021} - \frac{2019}{2020} (2 x) - \frac{2019}{2020} \cdot - 3 = 0$

Step 1.1.6

Cancel the common factor of $2$ .

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Step 1.1.6.1

Move the leading negative in $- \frac{2019}{2020}$ into the numerator.

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019}{2020} (2 x) - \frac{2019}{2020} \cdot - 3 = 0$

Step 1.1.6.2

Factor $2$ out of $2020$ .

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019}{2 (1010)} (2 x) - \frac{2019}{2020} \cdot - 3 = 0$

Step 1.1.6.3

Factor $2$ out of $2 x$ .

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019}{2 (1010)} (2 (x)) - \frac{2019}{2020} \cdot - 3 = 0$

Step 1.1.6.4

Cancel the common factor.

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019}{2 \cdot 1010} (2 x) - \frac{2019}{2020} \cdot - 3 = 0$

Step 1.1.6.5

Rewrite the expression.

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019}{1010} x - \frac{2019}{2020} \cdot - 3 = 0$

Step 1.1.7

Combine $\frac{- 2019}{1010}$ and $x$ .

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019 x}{1010} - \frac{2019}{2020} \cdot - 3 = 0$

Step 1.1.8

Multiply $- \frac{2019}{2020} \cdot - 3$ .

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Step 1.1.8.1

Multiply $- 3$ by $- 1$ .

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019 x}{1010} + 3 (\frac{2019}{2020}) = 0$

Step 1.1.8.2

Combine $3$ and $\frac{2019}{2020}$ .

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019 x}{1010} + \frac{3 \cdot 2019}{2020} = 0$

Step 1.1.8.3

Multiply $3$ by $2019$ .

$\frac{4040 x}{2021} - \frac{6060}{2021} + \frac{- 2019 x}{1010} + \frac{6057}{2020} = 0$

Step 1.1.9

Move the negative in front of the fraction.

$\frac{4040 x}{2021} - \frac{6060}{2021} - \frac{2019 x}{1010} + \frac{6057}{2020} = 0$

Step 1.2

To write $\frac{4040 x}{2021}$ as a fraction with a common denominator, multiply by $\frac{1010}{1010}$ .

$\frac{4040 x}{2021} \cdot \frac{1010}{1010} - \frac{2019 x}{1010} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.3

To write $- \frac{2019 x}{1010}$ as a fraction with a common denominator, multiply by $\frac{2021}{2021}$ .

$\frac{4040 x}{2021} \cdot \frac{1010}{1010} - \frac{2019 x}{1010} \cdot \frac{2021}{2021} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.4

Write each expression with a common denominator of $2041210$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{4040 x}{2021}$ by $\frac{1010}{1010}$ .

$\frac{4040 x \cdot 1010}{2021 \cdot 1010} - \frac{2019 x}{1010} \cdot \frac{2021}{2021} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.4.2

Multiply $2021$ by $1010$ .

$\frac{4040 x \cdot 1010}{2041210} - \frac{2019 x}{1010} \cdot \frac{2021}{2021} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.4.3

Multiply $\frac{2019 x}{1010}$ by $\frac{2021}{2021}$ .

$\frac{4040 x \cdot 1010}{2041210} - \frac{2019 x \cdot 2021}{1010 \cdot 2021} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.4.4

Multiply $1010$ by $2021$ .

$\frac{4040 x \cdot 1010}{2041210} - \frac{2019 x \cdot 2021}{2041210} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.5

Combine the numerators over the common denominator.

$\frac{4040 x \cdot 1010 - 2019 x \cdot 2021}{2041210} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.6

Find the common denominator.

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Step 1.6.1

Multiply $\frac{4040 x \cdot 1010 - 2019 x \cdot 2021}{2041210}$ by $\frac{2}{2}$ .

$\frac{4040 x \cdot 1010 - 2019 x \cdot 2021}{2041210} \cdot \frac{2}{2} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.6.2

Multiply $\frac{4040 x \cdot 1010 - 2019 x \cdot 2021}{2041210}$ by $\frac{2}{2}$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{2041210 \cdot 2} - \frac{6060}{2021} + \frac{6057}{2020} = 0$

Step 1.6.3

Multiply $\frac{6060}{2021}$ by $\frac{2020}{2020}$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{2041210 \cdot 2} - (\frac{6060}{2021} \cdot \frac{2020}{2020}) + \frac{6057}{2020} = 0$

Step 1.6.4

Multiply $\frac{6060}{2021}$ by $\frac{2020}{2020}$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{2041210 \cdot 2} - \frac{6060 \cdot 2020}{2021 \cdot 2020} + \frac{6057}{2020} = 0$

Step 1.6.5

Multiply $\frac{6057}{2020}$ by $\frac{2021}{2021}$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{2041210 \cdot 2} - \frac{6060 \cdot 2020}{2021 \cdot 2020} + \frac{6057}{2020} \cdot \frac{2021}{2021} = 0$

Step 1.6.6

Multiply $\frac{6057}{2020}$ by $\frac{2021}{2021}$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{2041210 \cdot 2} - \frac{6060 \cdot 2020}{2021 \cdot 2020} + \frac{6057 \cdot 2021}{2020 \cdot 2021} = 0$

Step 1.6.7

Reorder the factors of $2041210 \cdot 2$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{2 \cdot 2041210} - \frac{6060 \cdot 2020}{2021 \cdot 2020} + \frac{6057 \cdot 2021}{2020 \cdot 2021} = 0$

Step 1.6.8

Multiply $2$ by $2041210$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{4082420} - \frac{6060 \cdot 2020}{2021 \cdot 2020} + \frac{6057 \cdot 2021}{2020 \cdot 2021} = 0$

Step 1.6.9

Reorder the factors of $2021 \cdot 2020$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{4082420} - \frac{6060 \cdot 2020}{2020 \cdot 2021} + \frac{6057 \cdot 2021}{2020 \cdot 2021} = 0$

Step 1.6.10

Multiply $2020$ by $2021$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{4082420} - \frac{6060 \cdot 2020}{4082420} + \frac{6057 \cdot 2021}{2020 \cdot 2021} = 0$

Step 1.6.11

Multiply $2020$ by $2021$ .

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2}{4082420} - \frac{6060 \cdot 2020}{4082420} + \frac{6057 \cdot 2021}{4082420} = 0$

Step 1.7

Combine the numerators over the common denominator.

$\frac{(4040 x \cdot 1010 - 2019 x \cdot 2021) \cdot 2 - 6060 \cdot 2020 + 6057 \cdot 2021}{4082420} = 0$

Step 1.8

Simplify each term.

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Step 1.8.1

Simplify each term.

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Step 1.8.1.1

Multiply $1010$ by $4040$ .

$\frac{(4080400 x - 2019 x \cdot 2021) \cdot 2 - 6060 \cdot 2020 + 6057 \cdot 2021}{4082420} = 0$

Step 1.8.1.2

Multiply $2021$ by $- 2019$ .

$\frac{(4080400 x - 4080399 x) \cdot 2 - 6060 \cdot 2020 + 6057 \cdot 2021}{4082420} = 0$

Step 1.8.2

Subtract $4080399 x$ from $4080400 x$ .

$\frac{x \cdot 2 - 6060 \cdot 2020 + 6057 \cdot 2021}{4082420} = 0$

Step 1.8.3

Move $2$ to the left of $x$ .

$\frac{2 \cdot x - 6060 \cdot 2020 + 6057 \cdot 2021}{4082420} = 0$

Step 1.8.4

Multiply $- 6060$ by $2020$ .

$\frac{2 x - 12241200 + 6057 \cdot 2021}{4082420} = 0$

Step 1.8.5

Multiply $6057$ by $2021$ .

$\frac{2 x - 12241200 + 12241197}{4082420} = 0$

Step 1.9

Add $- 12241200$ and $12241197$ .

$\frac{2 x - 3}{4082420} = 0$

Step 2

Set the numerator equal to zero.

$2 x - 3 = 0$

Step 3

Solve the equation for $x$ .

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Step 3.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 3.2

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

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