Algebra Examples

$- x - 3 (- \frac{9}{4} x + \frac{3}{5}) + 5 = 4 x - 1$

Step 1

Simplify $- x - 3 (- \frac{9}{4} x + \frac{3}{5}) + 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Combine $x$ and $\frac{9}{4}$ .

$- x - 3 (- \frac{x \cdot 9}{4} + \frac{3}{5}) + 5 = 4 x - 1$

Step 1.1.1.2

Move $9$ to the left of $x$ .

$- x - 3 (- \frac{9 x}{4} + \frac{3}{5}) + 5 = 4 x - 1$

Step 1.1.2

Apply the distributive property.

$- x - 3 (- \frac{9 x}{4}) - 3 (\frac{3}{5}) + 5 = 4 x - 1$

Step 1.1.3

Multiply $- 3 (- \frac{9 x}{4})$ .

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Step 1.1.3.1

Multiply $- 1$ by $- 3$ .

$- x + 3 \frac{9 x}{4} - 3 (\frac{3}{5}) + 5 = 4 x - 1$

Step 1.1.3.2

Combine $3$ and $\frac{9 x}{4}$ .

$- x + \frac{3 (9 x)}{4} - 3 (\frac{3}{5}) + 5 = 4 x - 1$

Step 1.1.3.3

Multiply $9$ by $3$ .

$- x + \frac{27 x}{4} - 3 (\frac{3}{5}) + 5 = 4 x - 1$

Step 1.1.4

Multiply $- 3 (\frac{3}{5})$ .

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Step 1.1.4.1

Combine $- 3$ and $\frac{3}{5}$ .

$- x + \frac{27 x}{4} + \frac{- 3 \cdot 3}{5} + 5 = 4 x - 1$

Step 1.1.4.2

Multiply $- 3$ by $3$ .

$- x + \frac{27 x}{4} + \frac{- 9}{5} + 5 = 4 x - 1$

Step 1.1.5

Move the negative in front of the fraction.

$- x + \frac{27 x}{4} - \frac{9}{5} + 5 = 4 x - 1$

Step 1.2

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

$- x \cdot \frac{4}{4} + \frac{27 x}{4} - \frac{9}{5} + 5 = 4 x - 1$

Step 1.3

Combine $- x$ and $\frac{4}{4}$ .

$\frac{- x \cdot 4}{4} + \frac{27 x}{4} - \frac{9}{5} + 5 = 4 x - 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{- x \cdot 4 + 27 x}{4} - \frac{9}{5} + 5 = 4 x - 1$

Step 1.5

Find the common denominator.

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Step 1.5.1

Multiply $\frac{- x \cdot 4 + 27 x}{4}$ by $\frac{5}{5}$ .

$\frac{- x \cdot 4 + 27 x}{4} \cdot \frac{5}{5} - \frac{9}{5} + 5 = 4 x - 1$

Step 1.5.2

Multiply $\frac{- x \cdot 4 + 27 x}{4}$ by $\frac{5}{5}$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{4 \cdot 5} - \frac{9}{5} + 5 = 4 x - 1$

Step 1.5.3

Multiply $\frac{9}{5}$ by $\frac{4}{4}$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{4 \cdot 5} - (\frac{9}{5} \cdot \frac{4}{4}) + 5 = 4 x - 1$

Step 1.5.4

Multiply $\frac{9}{5}$ by $\frac{4}{4}$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{4 \cdot 5} - \frac{9 \cdot 4}{5 \cdot 4} + 5 = 4 x - 1$

Step 1.5.5

Write $5$ as a fraction with denominator $1$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{4 \cdot 5} - \frac{9 \cdot 4}{5 \cdot 4} + \frac{5}{1} = 4 x - 1$

Step 1.5.6

Multiply $\frac{5}{1}$ by $\frac{20}{20}$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{4 \cdot 5} - \frac{9 \cdot 4}{5 \cdot 4} + \frac{5}{1} \cdot \frac{20}{20} = 4 x - 1$

Step 1.5.7

Multiply $\frac{5}{1}$ by $\frac{20}{20}$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{4 \cdot 5} - \frac{9 \cdot 4}{5 \cdot 4} + \frac{5 \cdot 20}{20} = 4 x - 1$

Step 1.5.8

Multiply $4$ by $5$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{20} - \frac{9 \cdot 4}{5 \cdot 4} + \frac{5 \cdot 20}{20} = 4 x - 1$

Step 1.5.9

Reorder the factors of $5 \cdot 4$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{20} - \frac{9 \cdot 4}{4 \cdot 5} + \frac{5 \cdot 20}{20} = 4 x - 1$

Step 1.5.10

Multiply $4$ by $5$ .

$\frac{(- x \cdot 4 + 27 x) \cdot 5}{20} - \frac{9 \cdot 4}{20} + \frac{5 \cdot 20}{20} = 4 x - 1$

Step 1.6

Combine the numerators over the common denominator.

$\frac{(- x \cdot 4 + 27 x) \cdot 5 - 9 \cdot 4 + 5 \cdot 20}{20} = 4 x - 1$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $4$ by $- 1$ .

$\frac{(- 4 x + 27 x) \cdot 5 - 9 \cdot 4 + 5 \cdot 20}{20} = 4 x - 1$

Step 1.7.2

Add $- 4 x$ and $27 x$ .

$\frac{23 x \cdot 5 - 9 \cdot 4 + 5 \cdot 20}{20} = 4 x - 1$

Step 1.7.3

Multiply $5$ by $23$ .

$\frac{115 x - 9 \cdot 4 + 5 \cdot 20}{20} = 4 x - 1$

Step 1.7.4

Multiply $- 9$ by $4$ .

$\frac{115 x - 36 + 5 \cdot 20}{20} = 4 x - 1$

Step 1.7.5

Multiply $5$ by $20$ .

$\frac{115 x - 36 + 100}{20} = 4 x - 1$

Step 1.8

Add $- 36$ and $100$ .

$\frac{115 x + 64}{20} = 4 x - 1$

Step 2

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

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Step 2.1

Subtract $4 x$ from both sides of the equation.

$\frac{115 x + 64}{20} - 4 x = - 1$

Step 2.2

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{115 x + 64}{20} - 4 x \cdot \frac{20}{20} = - 1$

Step 2.3

Combine $- 4 x$ and $\frac{20}{20}$ .

$\frac{115 x + 64}{20} + \frac{- 4 x \cdot 20}{20} = - 1$

Step 2.4

Combine the numerators over the common denominator.

$\frac{115 x + 64 - 4 x \cdot 20}{20} = - 1$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $20$ by $- 4$ .

$\frac{115 x + 64 - 80 x}{20} = - 1$

Step 2.5.2

Subtract $80 x$ from $115 x$ .

$\frac{35 x + 64}{20} = - 1$

Step 3

Multiply both sides by $20$ .

$\frac{35 x + 64}{20} \cdot 20 = - 1 \cdot 20$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $20$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{35 x + 64}{20} \cdot 20 = - 1 \cdot 20$

Step 4.1.1.2

Rewrite the expression.

$35 x + 64 = - 1 \cdot 20$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 1$ by $20$ .

$35 x + 64 = - 20$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Subtract $64$ from both sides of the equation.

$35 x = - 20 - 64$

Step 5.1.2

Subtract $64$ from $- 20$ .

$35 x = - 84$

Step 5.2

Divide each term in $35 x = - 84$ by $35$ and simplify.

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Step 5.2.1

Divide each term in $35 x = - 84$ by $35$ .

$\frac{35 x}{35} = \frac{- 84}{35}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $35$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{35 x}{35} = \frac{- 84}{35}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 84}{35}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Cancel the common factor of $- 84$ and $35$ .

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Step 5.2.3.1.1

Factor $7$ out of $- 84$ .

$x = \frac{7 (- 12)}{35}$

Step 5.2.3.1.2

Cancel the common factors.

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Step 5.2.3.1.2.1

Factor $7$ out of $35$ .

$x = \frac{7 \cdot - 12}{7 \cdot 5}$

Step 5.2.3.1.2.2

Cancel the common factor.

$x = \frac{7 \cdot - 12}{7 \cdot 5}$

Step 5.2.3.1.2.3

Rewrite the expression.

$x = \frac{- 12}{5}$

Step 5.2.3.2

Move the negative in front of the fraction.

$x = - \frac{12}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{12}{5}$

Decimal Form:

$x = - 2.4$

Mixed Number Form:

$x = - 2 \frac{2}{5}$