Basic Math Examples

$\frac{3 x - 4}{5} - \frac{x + 1}{4} = \frac{2 x - 4}{3}$

Step 1

Multiply both sides by $3$ .

$(\frac{3 x - 4}{5} - \frac{x + 1}{4}) \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{3 x - 4}{5} - \frac{x + 1}{4}) \cdot 3$ .

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Step 2.1.1.1

To write $\frac{3 x - 4}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3 x - 4}{5} \cdot \frac{4}{4} - \frac{x + 1}{4}) \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.2

To write $- \frac{x + 1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{3 x - 4}{5} \cdot \frac{4}{4} - \frac{x + 1}{4} \cdot \frac{5}{5}) \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.3.1

Multiply $\frac{3 x - 4}{5}$ by $\frac{4}{4}$ .

$(\frac{(3 x - 4) \cdot 4}{5 \cdot 4} - \frac{x + 1}{4} \cdot \frac{5}{5}) \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.3.2

Multiply $5$ by $4$ .

$(\frac{(3 x - 4) \cdot 4}{20} - \frac{x + 1}{4} \cdot \frac{5}{5}) \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.3.3

Multiply $\frac{x + 1}{4}$ by $\frac{5}{5}$ .

$(\frac{(3 x - 4) \cdot 4}{20} - \frac{(x + 1) \cdot 5}{4 \cdot 5}) \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.3.4

Multiply $4$ by $5$ .

$(\frac{(3 x - 4) \cdot 4}{20} - \frac{(x + 1) \cdot 5}{20}) \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{(3 x - 4) \cdot 4 - (x + 1) \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Apply the distributive property.

$\frac{3 x \cdot 4 - 4 \cdot 4 - (x + 1) \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.2

Multiply $4$ by $3$ .

$\frac{12 x - 4 \cdot 4 - (x + 1) \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.3

Multiply $- 4$ by $4$ .

$\frac{12 x - 16 - (x + 1) \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.4

Apply the distributive property.

$\frac{12 x - 16 + (- x - 1 \cdot 1) \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.5

Multiply $- 1$ by $1$ .

$\frac{12 x - 16 + (- x - 1) \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.6

Apply the distributive property.

$\frac{12 x - 16 - x \cdot 5 - 1 \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.7

Multiply $5$ by $- 1$ .

$\frac{12 x - 16 - 5 x - 1 \cdot 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.8

Multiply $- 1$ by $5$ .

$\frac{12 x - 16 - 5 x - 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.9

Subtract $5 x$ from $12 x$ .

$\frac{7 x - 16 - 5}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.10

Subtract $5$ from $- 16$ .

$\frac{7 x - 21}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.11

Factor $7$ out of $7 x - 21$ .

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Step 2.1.1.5.11.1

Factor $7$ out of $7 x$ .

$\frac{7 (x) - 21}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.11.2

Factor $7$ out of $- 21$ .

$\frac{7 x + 7 \cdot - 3}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.5.11.3

Factor $7$ out of $7 x + 7 \cdot - 3$ .

$\frac{7 (x - 3)}{20} \cdot 3 = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.6

Multiply $\frac{7 (x - 3)}{20} \cdot 3$ .

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Step 2.1.1.6.1

Combine $\frac{7 (x - 3)}{20}$ and $3$ .

$\frac{7 (x - 3) \cdot 3}{20} = \frac{2 x - 4}{3} \cdot 3$

Step 2.1.1.6.2

Multiply $3$ by $7$ .

$\frac{21 (x - 3)}{20} = \frac{2 x - 4}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2 x - 4}{3} \cdot 3$ .

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Step 2.2.1.1

Factor $2$ out of $2 x - 4$ .

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Step 2.2.1.1.1

Factor $2$ out of $2 x$ .

$\frac{21 (x - 3)}{20} = \frac{2 (x) - 4}{3} \cdot 3$

Step 2.2.1.1.2

Factor $2$ out of $- 4$ .

$\frac{21 (x - 3)}{20} = \frac{2 x + 2 \cdot - 2}{3} \cdot 3$

Step 2.2.1.1.3

Factor $2$ out of $2 x + 2 \cdot - 2$ .

$\frac{21 (x - 3)}{20} = \frac{2 (x - 2)}{3} \cdot 3$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Cancel the common factor.

$\frac{21 (x - 3)}{20} = \frac{2 (x - 2)}{3} \cdot 3$

Step 2.2.1.2.2

Rewrite the expression.

$\frac{21 (x - 3)}{20} = 2 (x - 2)$

Step 2.2.1.3

Apply the distributive property.

$\frac{21 (x - 3)}{20} = 2 x + 2 \cdot - 2$

Step 2.2.1.4

Multiply $2$ by $- 2$ .

$\frac{21 (x - 3)}{20} = 2 x - 4$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $20$ .

$\frac{21 (x - 3)}{20} \cdot 20 = (2 x - 4) \cdot 20$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{21 (x - 3)}{20} \cdot 20$ .

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Step 3.2.1.1.1

Cancel the common factor of $20$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{21 (x - 3)}{20} \cdot 20 = (2 x - 4) \cdot 20$

Step 3.2.1.1.1.2

Rewrite the expression.

$21 (x - 3) = (2 x - 4) \cdot 20$

Step 3.2.1.1.2

Apply the distributive property.

$21 x + 21 \cdot - 3 = (2 x - 4) \cdot 20$

Step 3.2.1.1.3

Multiply $21$ by $- 3$ .

$21 x - 63 = (2 x - 4) \cdot 20$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(2 x - 4) \cdot 20$ .

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Step 3.2.2.1.1

Apply the distributive property.

$21 x - 63 = 2 x \cdot 20 - 4 \cdot 20$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $20$ by $2$ .

$21 x - 63 = 40 x - 4 \cdot 20$

Step 3.2.2.1.2.2

Multiply $- 4$ by $20$ .

$21 x - 63 = 40 x - 80$

Step 3.3

Solve for $x$ .

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Step 3.3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.3.1.1

Subtract $40 x$ from both sides of the equation.

$21 x - 63 - 40 x = - 80$

Step 3.3.1.2

Subtract $40 x$ from $21 x$ .

$- 19 x - 63 = - 80$

Step 3.3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.3.2.1

Add $63$ to both sides of the equation.

$- 19 x = - 80 + 63$

Step 3.3.2.2

Add $- 80$ and $63$ .

$- 19 x = - 17$

Step 3.3.3

Divide each term in $- 19 x = - 17$ by $- 19$ and simplify.

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Step 3.3.3.1

Divide each term in $- 19 x = - 17$ by $- 19$ .

$\frac{- 19 x}{- 19} = \frac{- 17}{- 19}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 19$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 19 x}{- 19} = \frac{- 17}{- 19}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 17}{- 19}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{17}{19}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{19}$

Decimal Form:

$x = 0.89473684 \dots$