Algebra Examples

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

Step 1

Simplify $- 1 - (- 3 x - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $- 3$ by $- 1$ .

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

Step 1.1.3

Multiply $- 1$ by $- 1$ .

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

Step 1.2

Combine the opposite terms in $- 1 + 3 x + 1$ .

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Step 1.2.1

Add $- 1$ and $1$ .

$3 x + 0 = - \frac{3}{5} \cdot (x - \frac{3}{2})$

Step 1.2.2

Add $3 x$ and $0$ .

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

Step 2

Simplify $- \frac{3}{5} \cdot (x - \frac{3}{2})$ .

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Step 2.1

Apply the distributive property.

$3 x = - \frac{3}{5} x - \frac{3}{5} (- \frac{3}{2})$

Step 2.2

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

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

Step 2.3

Multiply $- \frac{3}{5} (- \frac{3}{2})$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.3.2

Multiply $\frac{3}{5}$ by $1$ .

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

Step 2.3.3

Multiply $\frac{3}{5}$ by $\frac{3}{2}$ .

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

Step 2.3.4

Multiply $3$ by $3$ .

$3 x = - \frac{x \cdot 3}{5} + \frac{9}{5 \cdot 2}$

Step 2.3.5

Multiply $5$ by $2$ .

$3 x = - \frac{x \cdot 3}{5} + \frac{9}{10}$

Step 2.4

Move $3$ to the left of $x$ .

$3 x = - \frac{3 x}{5} + \frac{9}{10}$

Step 3

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

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Step 3.1

Add $\frac{3 x}{5}$ to both sides of the equation.

$3 x + \frac{3 x}{5} = \frac{9}{10}$

Step 3.2

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

$3 x \cdot \frac{5}{5} + \frac{3 x}{5} = \frac{9}{10}$

Step 3.3

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

$\frac{3 x \cdot 5}{5} + \frac{3 x}{5} = \frac{9}{10}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 5 + 3 x}{5} = \frac{9}{10}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $3 x$ out of $3 x \cdot 5 + 3 x$ .

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Step 3.5.1.1

Factor $3 x$ out of $3 x \cdot 5$ .

$\frac{3 x (5) + 3 x}{5} = \frac{9}{10}$

Step 3.5.1.2

Factor $3 x$ out of $3 x$ .

$\frac{3 x (5) + 3 x (1)}{5} = \frac{9}{10}$

Step 3.5.1.3

Factor $3 x$ out of $3 x (5) + 3 x (1)$ .

$\frac{3 x (5 + 1)}{5} = \frac{9}{10}$

Step 3.5.2

Add $5$ and $1$ .

$\frac{3 x \cdot 6}{5} = \frac{9}{10}$

Step 3.5.3

Multiply $6$ by $3$ .

$\frac{18 x}{5} = \frac{9}{10}$

Step 4

Multiply both sides of the equation by $\frac{5}{18}$ .

$\frac{5}{18} \cdot \frac{18 x}{5} = \frac{5}{18} \cdot \frac{9}{10}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{18} \cdot \frac{18 x}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{18} \cdot \frac{18 x}{5} = \frac{5}{18} \cdot \frac{9}{10}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{18} (18 x) = \frac{5}{18} \cdot \frac{9}{10}$

Step 5.1.1.2

Cancel the common factor of $18$ .

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Step 5.1.1.2.1

Factor $18$ out of $18 x$ .

$\frac{1}{18} (18 (x)) = \frac{5}{18} \cdot \frac{9}{10}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{18} (18 x) = \frac{5}{18} \cdot \frac{9}{10}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{5}{18} \cdot \frac{9}{10}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{18} \cdot \frac{9}{10}$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Factor $5$ out of $10$ .

$x = \frac{5}{18} \cdot \frac{9}{5 (2)}$

Step 5.2.1.1.2

Cancel the common factor.

$x = \frac{5}{18} \cdot \frac{9}{5 \cdot 2}$

Step 5.2.1.1.3

Rewrite the expression.

$x = \frac{1}{18} \cdot \frac{9}{2}$

Step 5.2.1.2

Cancel the common factor of $9$ .

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Step 5.2.1.2.1

Factor $9$ out of $18$ .

$x = \frac{1}{9 (2)} \cdot \frac{9}{2}$

Step 5.2.1.2.2

Cancel the common factor.

$x = \frac{1}{9 \cdot 2} \cdot \frac{9}{2}$

Step 5.2.1.2.3

Rewrite the expression.

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

Step 5.2.1.3

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

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

Step 5.2.1.4

Multiply $2$ by $2$ .

$x = \frac{1}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}$

Decimal Form:

$x = 0.25$