Algebra Examples

$6 + \frac{4}{5} x = \frac{9}{10} x$

Step 1

Combine $\frac{4}{5}$ and $x$ .

$6 + \frac{4 x}{5} = \frac{9}{10} x$

Step 2

Combine $\frac{9}{10}$ and $x$ .

$6 + \frac{4 x}{5} = \frac{9 x}{10}$

Step 3

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

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Step 3.1

Subtract $\frac{9 x}{10}$ from both sides of the equation.

$6 + \frac{4 x}{5} - \frac{9 x}{10} = 0$

Step 3.2

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 + \frac{4 x}{5} \cdot \frac{2}{2} - \frac{9 x}{10} = 0$

Step 3.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{4 x}{5}$ by $\frac{2}{2}$ .

$6 + \frac{4 x \cdot 2}{5 \cdot 2} - \frac{9 x}{10} = 0$

Step 3.3.2

Multiply $5$ by $2$ .

$6 + \frac{4 x \cdot 2}{10} - \frac{9 x}{10} = 0$

Step 3.4

Combine the numerators over the common denominator.

$6 + \frac{4 x \cdot 2 - 9 x}{10} = 0$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $4 x \cdot 2 - 9 x$ .

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Step 3.5.1.1.1

Factor $x$ out of $4 x \cdot 2$ .

$6 + \frac{x (4 \cdot 2) - 9 x}{10} = 0$

Step 3.5.1.1.2

Factor $x$ out of $- 9 x$ .

$6 + \frac{x (4 \cdot 2) + x \cdot - 9}{10} = 0$

Step 3.5.1.1.3

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 9$ .

$6 + \frac{x (4 \cdot 2 - 9)}{10} = 0$

Step 3.5.1.2

Multiply $4$ by $2$ .

$6 + \frac{x (8 - 9)}{10} = 0$

Step 3.5.1.3

Subtract $9$ from $8$ .

$6 + \frac{x \cdot - 1}{10} = 0$

Step 3.5.2

Move $- 1$ to the left of $x$ .

$6 + \frac{- 1 \cdot x}{10} = 0$

Step 3.5.3

Move the negative in front of the fraction.

$6 - \frac{x}{10} = 0$

Step 4

Subtract $6$ from both sides of the equation.

$- \frac{x}{10} = - 6$

Step 5

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{x}{10}) = - 10 \cdot - 6$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $10$ .

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Step 6.1.1.1.1

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

$- 10 \frac{- x}{10} = - 10 \cdot - 6$

Step 6.1.1.1.2

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- x}{10} = - 10 \cdot - 6$

Step 6.1.1.1.3

Cancel the common factor.

$10 \cdot - 1 \frac{- x}{10} = - 10 \cdot - 6$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 10 \cdot - 6$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 10 \cdot - 6$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 10 \cdot - 6$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 10$ by $- 6$ .

$x = 60$