Algebra Examples

$7 x - 2 (x - 1) = 1 - \frac{9}{10} (- 5 x + \frac{5}{3})$

Step 1

Simplify $7 x - 2 (x - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$7 x - 2 x - 2 \cdot - 1 = 1 - \frac{9}{10} \cdot (- 5 x + \frac{5}{3})$

Step 1.1.2

Multiply $- 2$ by $- 1$ .

$7 x - 2 x + 2 = 1 - \frac{9}{10} \cdot (- 5 x + \frac{5}{3})$

Step 1.2

Subtract $2 x$ from $7 x$ .

$5 x + 2 = 1 - \frac{9}{10} \cdot (- 5 x + \frac{5}{3})$

Step 2

Simplify $1 - \frac{9}{10} \cdot (- 5 x + \frac{5}{3})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$5 x + 2 = 1 - \frac{9}{10} (- 5 x) - \frac{9}{10} \cdot \frac{5}{3}$

Step 2.1.2

Cancel the common factor of $5$ .

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Step 2.1.2.1

Move the leading negative in $- \frac{9}{10}$ into the numerator.

$5 x + 2 = 1 + \frac{- 9}{10} (- 5 x) - \frac{9}{10} \cdot \frac{5}{3}$

Step 2.1.2.2

Factor $5$ out of $10$ .

$5 x + 2 = 1 + \frac{- 9}{5 (2)} (- 5 x) - \frac{9}{10} \cdot \frac{5}{3}$

Step 2.1.2.3

Factor $5$ out of $- 5 x$ .

$5 x + 2 = 1 + \frac{- 9}{5 (2)} (5 (- x)) - \frac{9}{10} \cdot \frac{5}{3}$

Step 2.1.2.4

Cancel the common factor.

$5 x + 2 = 1 + \frac{- 9}{5 \cdot 2} (5 (- x)) - \frac{9}{10} \cdot \frac{5}{3}$

Step 2.1.2.5

Rewrite the expression.

$5 x + 2 = 1 + \frac{- 9}{2} (- x) - \frac{9}{10} \cdot \frac{5}{3}$

Step 2.1.3

Combine $\frac{- 9}{2}$ and $x$ .

$5 x + 2 = 1 - \frac{- 9 x}{2} - \frac{9}{10} \cdot \frac{5}{3}$

Step 2.1.4

Cancel the common factor of $3$ .

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Step 2.1.4.1

Move the leading negative in $- \frac{9}{10}$ into the numerator.

$5 x + 2 = 1 - \frac{- 9 x}{2} + \frac{- 9}{10} \cdot \frac{5}{3}$

Step 2.1.4.2

Factor $3$ out of $- 9$ .

$5 x + 2 = 1 - \frac{- 9 x}{2} + \frac{3 (- 3)}{10} \cdot \frac{5}{3}$

Step 2.1.4.3

Cancel the common factor.

$5 x + 2 = 1 - \frac{- 9 x}{2} + \frac{3 \cdot - 3}{10} \cdot \frac{5}{3}$

Step 2.1.4.4

Rewrite the expression.

$5 x + 2 = 1 - \frac{- 9 x}{2} + \frac{- 3}{10} \cdot 5$

Step 2.1.5

Cancel the common factor of $5$ .

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Step 2.1.5.1

Factor $5$ out of $10$ .

$5 x + 2 = 1 - \frac{- 9 x}{2} + \frac{- 3}{5 (2)} \cdot 5$

Step 2.1.5.2

Cancel the common factor.

$5 x + 2 = 1 - \frac{- 9 x}{2} + \frac{- 3}{5 \cdot 2} \cdot 5$

Step 2.1.5.3

Rewrite the expression.

$5 x + 2 = 1 - \frac{- 9 x}{2} + \frac{- 3}{2}$

Step 2.1.6

Simplify each term.

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Step 2.1.6.1

Move the negative in front of the fraction.

$5 x + 2 = 1 - - \frac{9 x}{2} + \frac{- 3}{2}$

Step 2.1.6.2

Multiply $- - \frac{9 x}{2}$ .

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Step 2.1.6.2.1

Multiply $- 1$ by $- 1$ .

$5 x + 2 = 1 + 1 \frac{9 x}{2} + \frac{- 3}{2}$

Step 2.1.6.2.2

Multiply $\frac{9 x}{2}$ by $1$ .

$5 x + 2 = 1 + \frac{9 x}{2} + \frac{- 3}{2}$

Step 2.1.6.3

Move the negative in front of the fraction.

$5 x + 2 = 1 + \frac{9 x}{2} - \frac{3}{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Subtract $3$ from $2$ .

$5 x + 2 = \frac{9 x}{2} + \frac{- 1}{2}$

Step 2.2.4

Move the negative in front of the fraction.

$5 x + 2 = \frac{9 x}{2} - \frac{1}{2}$

Step 3

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

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Step 3.1

Subtract $\frac{9 x}{2}$ from both sides of the equation.

$5 x + 2 - \frac{9 x}{2} = - \frac{1}{2}$

Step 3.2

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

$5 x \cdot \frac{2}{2} - \frac{9 x}{2} + 2 = - \frac{1}{2}$

Step 3.3

Combine $5 x$ and $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{2} - \frac{9 x}{2} + 2 = - \frac{1}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 - 9 x}{2} + 2 = - \frac{1}{2}$

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 $5 x \cdot 2 - 9 x$ .

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Step 3.5.1.1.1

Factor $x$ out of $5 x \cdot 2$ .

$\frac{x (5 \cdot 2) - 9 x}{2} + 2 = - \frac{1}{2}$

Step 3.5.1.1.2

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

$\frac{x (5 \cdot 2) + x \cdot - 9}{2} + 2 = - \frac{1}{2}$

Step 3.5.1.1.3

Factor $x$ out of $x (5 \cdot 2) + x \cdot - 9$ .

$\frac{x (5 \cdot 2 - 9)}{2} + 2 = - \frac{1}{2}$

Step 3.5.1.2

Multiply $5$ by $2$ .

$\frac{x (10 - 9)}{2} + 2 = - \frac{1}{2}$

Step 3.5.1.3

Subtract $9$ from $10$ .

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

Step 3.5.2

Multiply $x$ by $1$ .

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

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 2$ by $2$ .

$\frac{x}{2} = \frac{- 1 - 4}{2}$

Step 4.5.2

Subtract $4$ from $- 1$ .

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

Step 4.6

Move the negative in front of the fraction.

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

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 5$