Algebra Examples

$- 1 - (3 x - \frac{1}{2}) = - \frac{6}{5} (x - 1) + 5 x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \frac{6}{5} \cdot (x - 1) + 5 x = - 1 - (3 x - \frac{1}{2})$

Step 2

Simplify $- \frac{6}{5} \cdot (x - 1) + 5 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- \frac{6}{5} x - \frac{6}{5} \cdot - 1 + 5 x = - 1 - (3 x - \frac{1}{2})$

Step 2.1.2

Combine $x$ and $\frac{6}{5}$ .

$- \frac{x \cdot 6}{5} - \frac{6}{5} \cdot - 1 + 5 x = - 1 - (3 x - \frac{1}{2})$

Step 2.1.3

Multiply $- \frac{6}{5} \cdot - 1$ .

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Step 2.1.3.1

Multiply $- 1$ by $- 1$ .

$- \frac{x \cdot 6}{5} + 1 (\frac{6}{5}) + 5 x = - 1 - (3 x - \frac{1}{2})$

Step 2.1.3.2

Multiply $\frac{6}{5}$ by $1$ .

$- \frac{x \cdot 6}{5} + \frac{6}{5} + 5 x = - 1 - (3 x - \frac{1}{2})$

Step 2.1.4

Move $6$ to the left of $x$ .

$- \frac{6 x}{5} + \frac{6}{5} + 5 x = - 1 - (3 x - \frac{1}{2})$

Step 2.2

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

$- \frac{6 x}{5} + 5 x \cdot \frac{5}{5} + \frac{6}{5} = - 1 - (3 x - \frac{1}{2})$

Step 2.3

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

$- \frac{6 x}{5} + \frac{5 x \cdot 5}{5} + \frac{6}{5} = - 1 - (3 x - \frac{1}{2})$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 6 x + 5 x \cdot 5}{5} + \frac{6}{5} = - 1 - (3 x - \frac{1}{2})$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 6 x + 5 x \cdot 5 + 6}{5} = - 1 - (3 x - \frac{1}{2})$

Step 2.6

Multiply $5$ by $5$ .

$\frac{- 6 x + 25 x + 6}{5} = - 1 - (3 x - \frac{1}{2})$

Step 2.7

Add $- 6 x$ and $25 x$ .

$\frac{19 x + 6}{5} = - 1 - (3 x - \frac{1}{2})$

Step 3

Simplify $- 1 - (3 x - \frac{1}{2})$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$\frac{19 x + 6}{5} = - 1 - (3 x) - - \frac{1}{2}$

Step 3.1.2

Multiply $3$ by $- 1$ .

$\frac{19 x + 6}{5} = - 1 - 3 x - - \frac{1}{2}$

Step 3.1.3

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

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Step 3.1.3.1

Multiply $- 1$ by $- 1$ .

$\frac{19 x + 6}{5} = - 1 - 3 x + 1 (\frac{1}{2})$

Step 3.1.3.2

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

$\frac{19 x + 6}{5} = - 1 - 3 x + \frac{1}{2}$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{19 x + 6}{5} = - 3 x - 1 \cdot \frac{2}{2} + \frac{1}{2}$

Step 3.3

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{19 x + 6}{5} = - 3 x + \frac{- 1 \cdot 2}{2} + \frac{1}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{19 x + 6}{5} = - 3 x + \frac{- 1 \cdot 2 + 1}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $2$ .

$\frac{19 x + 6}{5} = - 3 x + \frac{- 2 + 1}{2}$

Step 3.5.2

Add $- 2$ and $1$ .

$\frac{19 x + 6}{5} = - 3 x + \frac{- 1}{2}$

Step 3.6

Move the negative in front of the fraction.

$\frac{19 x + 6}{5} = - 3 x - \frac{1}{2}$

Step 4

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

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Step 4.1

Add $3 x$ to both sides of the equation.

$\frac{19 x + 6}{5} + 3 x = - \frac{1}{2}$

Step 4.2

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

$\frac{19 x + 6}{5} + 3 x \cdot \frac{5}{5} = - \frac{1}{2}$

Step 4.3

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

$\frac{19 x + 6}{5} + \frac{3 x \cdot 5}{5} = - \frac{1}{2}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{19 x + 6 + 3 x \cdot 5}{5} = - \frac{1}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $5$ by $3$ .

$\frac{19 x + 6 + 15 x}{5} = - \frac{1}{2}$

Step 4.5.2

Add $19 x$ and $15 x$ .

$\frac{34 x + 6}{5} = - \frac{1}{2}$

Step 4.5.3

Factor $2$ out of $34 x + 6$ .

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Step 4.5.3.1

Factor $2$ out of $34 x$ .

$\frac{2 (17 x) + 6}{5} = - \frac{1}{2}$

Step 4.5.3.2

Factor $2$ out of $6$ .

$\frac{2 (17 x) + 2 (3)}{5} = - \frac{1}{2}$

Step 4.5.3.3

Factor $2$ out of $2 (17 x) + 2 (3)$ .

$\frac{2 (17 x + 3)}{5} = - \frac{1}{2}$

Step 5

Multiply both sides by $5$ .

$\frac{2 (17 x + 3)}{5} \cdot 5 = - \frac{1}{2} \cdot 5$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{2 (17 x + 3)}{5} \cdot 5$ .

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Step 6.1.1.1

Cancel the common factor of $5$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{2 (17 x + 3)}{5} \cdot 5 = - \frac{1}{2} \cdot 5$

Step 6.1.1.1.2

Rewrite the expression.

$2 (17 x + 3) = - \frac{1}{2} \cdot 5$

Step 6.1.1.2

Apply the distributive property.

$2 (17 x) + 2 \cdot 3 = - \frac{1}{2} \cdot 5$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $17$ by $2$ .

$34 x + 2 \cdot 3 = - \frac{1}{2} \cdot 5$

Step 6.1.1.3.2

Multiply $2$ by $3$ .

$34 x + 6 = - \frac{1}{2} \cdot 5$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{1}{2} \cdot 5$ .

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Step 6.2.1.1

Multiply $- \frac{1}{2} \cdot 5$ .

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Step 6.2.1.1.1

Multiply $5$ by $- 1$ .

$34 x + 6 = - 5 (\frac{1}{2})$

Step 6.2.1.1.2

Combine $- 5$ and $\frac{1}{2}$ .

$34 x + 6 = \frac{- 5}{2}$

Step 6.2.1.2

Move the negative in front of the fraction.

$34 x + 6 = - \frac{5}{2}$

Step 7

Solve for $x$ .

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Step 7.1

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

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Step 7.1.1

Subtract $6$ from both sides of the equation.

$34 x = - \frac{5}{2} - 6$

Step 7.1.2

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$34 x = - \frac{5}{2} - 6 \cdot \frac{2}{2}$

Step 7.1.3

Combine $- 6$ and $\frac{2}{2}$ .

$34 x = - \frac{5}{2} + \frac{- 6 \cdot 2}{2}$

Step 7.1.4

Combine the numerators over the common denominator.

$34 x = \frac{- 5 - 6 \cdot 2}{2}$

Step 7.1.5

Simplify the numerator.

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Step 7.1.5.1

Multiply $- 6$ by $2$ .

$34 x = \frac{- 5 - 12}{2}$

Step 7.1.5.2

Subtract $12$ from $- 5$ .

$34 x = \frac{- 17}{2}$

Step 7.1.6

Move the negative in front of the fraction.

$34 x = - \frac{17}{2}$

Step 7.2

Divide each term in $34 x = - \frac{17}{2}$ by $34$ and simplify.

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Step 7.2.1

Divide each term in $34 x = - \frac{17}{2}$ by $34$ .

$\frac{34 x}{34} = \frac{- \frac{17}{2}}{34}$

Step 7.2.2

Simplify the left side.

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Step 7.2.2.1

Cancel the common factor of $34$ .

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Step 7.2.2.1.1

Cancel the common factor.

$\frac{34 x}{34} = \frac{- \frac{17}{2}}{34}$

Step 7.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{17}{2}}{34}$

Step 7.2.3

Simplify the right side.

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Step 7.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{17}{2} \cdot \frac{1}{34}$

Step 7.2.3.2

Cancel the common factor of $17$ .

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Step 7.2.3.2.1

Move the leading negative in $- \frac{17}{2}$ into the numerator.

$x = \frac{- 17}{2} \cdot \frac{1}{34}$

Step 7.2.3.2.2

Factor $17$ out of $- 17$ .

$x = \frac{17 (- 1)}{2} \cdot \frac{1}{34}$

Step 7.2.3.2.3

Factor $17$ out of $34$ .

$x = \frac{17 \cdot - 1}{2} \cdot \frac{1}{17 \cdot 2}$

Step 7.2.3.2.4

Cancel the common factor.

$x = \frac{17 \cdot - 1}{2} \cdot \frac{1}{17 \cdot 2}$

Step 7.2.3.2.5

Rewrite the expression.

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

Step 7.2.3.3

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

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

Step 7.2.3.4

Simplify the expression.

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Step 7.2.3.4.1

Multiply $2$ by $2$ .

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

Step 7.2.3.4.2

Move the negative in front of the fraction.

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.25$