Pre-Algebra Examples

$\frac{3}{10} x - 2 x + \frac{6}{5} = \frac{3}{5}$

Step 1

Simplify $\frac{3}{10} x - 2 x + \frac{6}{5}$ .

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Step 1.1

Combine $\frac{3}{10}$ and $x$ .

$\frac{3 x}{10} - 2 x + \frac{6}{5} = \frac{3}{5}$

Step 1.2

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{3 x}{10} - 2 x \cdot \frac{10}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $- 2 x$ and $\frac{10}{10}$ .

$\frac{3 x}{10} + \frac{- 2 x \cdot 10}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{3 x - 2 x \cdot 10}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $x$ out of $3 x - 2 x \cdot 10$ .

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Step 1.4.1.1.1

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - 2 x \cdot 10}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.4.1.1.2

Factor $x$ out of $- 2 x \cdot 10$ .

$\frac{x \cdot 3 + x (- 2 \cdot 10)}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.4.1.1.3

Factor $x$ out of $x \cdot 3 + x (- 2 \cdot 10)$ .

$\frac{x (3 - 2 \cdot 10)}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.4.1.2

Multiply $- 2$ by $10$ .

$\frac{x (3 - 20)}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.4.1.3

Subtract $20$ from $3$ .

$\frac{x \cdot - 17}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.4.2

Move $- 17$ to the left of $x$ .

$\frac{- 17 \cdot x}{10} + \frac{6}{5} = \frac{3}{5}$

Step 1.4.3

Move the negative in front of the fraction.

$- \frac{17 x}{10} + \frac{6}{5} = \frac{3}{5}$

Step 2

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

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Step 2.1

Subtract $\frac{6}{5}$ from both sides of the equation.

$- \frac{17 x}{10} = \frac{3}{5} - \frac{6}{5}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{17 x}{10} = \frac{3 - 6}{5}$

Step 2.3

Subtract $6$ from $3$ .

$- \frac{17 x}{10} = \frac{- 3}{5}$

Step 2.4

Move the negative in front of the fraction.

$- \frac{17 x}{10} = - \frac{3}{5}$

Step 3

Multiply both sides of the equation by $- \frac{10}{17}$ .

$- \frac{10}{17} (- \frac{17 x}{10}) = - \frac{10}{17} (- \frac{3}{5})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{10}{17} (- \frac{17 x}{10})$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{10}{17}$ into the numerator.

$\frac{- 10}{17} (- \frac{17 x}{10}) = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.1.2

Move the leading negative in $- \frac{17 x}{10}$ into the numerator.

$\frac{- 10}{17} \cdot \frac{- 17 x}{10} = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.1.3

Factor $10$ out of $- 10$ .

$\frac{10 (- 1)}{17} \cdot \frac{- 17 x}{10} = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{10 \cdot - 1}{17} \cdot \frac{- 17 x}{10} = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{17} (- 17 x) = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.2

Cancel the common factor of $17$ .

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Step 4.1.1.2.1

Factor $17$ out of $- 17 x$ .

$\frac{- 1}{17} (17 (- x)) = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{17} (17 (- x)) = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{10}{17} (- \frac{3}{5})$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{10}{17} (- \frac{3}{5})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{10}{17} (- \frac{3}{5})$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{10}{17}$ into the numerator.

$x = \frac{- 10}{17} (- \frac{3}{5})$

Step 4.2.1.1.2

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$x = \frac{- 10}{17} \cdot \frac{- 3}{5}$

Step 4.2.1.1.3

Factor $5$ out of $- 10$ .

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

Step 4.2.1.1.4

Cancel the common factor.

$x = \frac{5 \cdot - 2}{17} \cdot \frac{- 3}{5}$

Step 4.2.1.1.5

Rewrite the expression.

$x = \frac{- 2}{17} \cdot - 3$

Step 4.2.1.2

Combine $\frac{- 2}{17}$ and $- 3$ .

$x = \frac{- 2 \cdot - 3}{17}$

Step 4.2.1.3

Multiply $- 2$ by $- 3$ .

$x = \frac{6}{17}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{17}$

Decimal Form:

$x = 0.35294117 \dots$