Algebra Examples

$x - (5 x - 1) - \frac{7 - 5 x}{10} = 1$

Step 1

Simplify $x - (5 x - 1) - \frac{7 - 5 x}{10}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

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

$\frac{x}{1} - (5 x - 1) - \frac{7 - 5 x}{10} = 1$

Step 1.1.2

Multiply $\frac{x}{1}$ by $\frac{10}{10}$ .

$\frac{x}{1} \cdot \frac{10}{10} - (5 x - 1) - \frac{7 - 5 x}{10} = 1$

Step 1.1.3

Multiply $\frac{x}{1}$ by $\frac{10}{10}$ .

$\frac{x \cdot 10}{10} - (5 x - 1) - \frac{7 - 5 x}{10} = 1$

Step 1.1.4

Write $- (5 x - 1)$ as a fraction with denominator $1$ .

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

Step 1.1.5

Multiply $\frac{- (5 x - 1)}{1}$ by $\frac{10}{10}$ .

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

Step 1.1.6

Multiply $\frac{- (5 x - 1)}{1}$ by $\frac{10}{10}$ .

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

Step 1.2

Combine the numerators over the common denominator.

$\frac{x \cdot 10 - (5 x - 1) \cdot 10 - (7 - 5 x)}{10} = 1$

Step 1.3

Simplify each term.

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Step 1.3.1

Move $10$ to the left of $x$ .

$\frac{10 \cdot x - (5 x - 1) \cdot 10 - (7 - 5 x)}{10} = 1$

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Multiply $5$ by $- 1$ .

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

Step 1.3.4

Multiply $- 1$ by $- 1$ .

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

Step 1.3.5

Apply the distributive property.

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

Step 1.3.6

Multiply $10$ by $- 5$ .

$\frac{10 x - 50 x + 1 \cdot 10 - (7 - 5 x)}{10} = 1$

Step 1.3.7

Multiply $10$ by $1$ .

$\frac{10 x - 50 x + 10 - (7 - 5 x)}{10} = 1$

Step 1.3.8

Apply the distributive property.

$\frac{10 x - 50 x + 10 - 1 \cdot 7 - (- 5 x)}{10} = 1$

Step 1.3.9

Multiply $- 1$ by $7$ .

$\frac{10 x - 50 x + 10 - 7 - (- 5 x)}{10} = 1$

Step 1.3.10

Multiply $- 5$ by $- 1$ .

$\frac{10 x - 50 x + 10 - 7 + 5 x}{10} = 1$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $50 x$ from $10 x$ .

$\frac{- 40 x + 10 - 7 + 5 x}{10} = 1$

Step 1.4.2

Add $- 40 x$ and $5 x$ .

$\frac{- 35 x + 10 - 7}{10} = 1$

Step 1.4.3

Subtract $7$ from $10$ .

$\frac{- 35 x + 3}{10} = 1$

Step 1.4.4

Factor $- 1$ out of $- 35 x$ .

$\frac{- (35 x) + 3}{10} = 1$

Step 1.4.5

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{- (35 x) - 1 (- 3)}{10} = 1$

Step 1.4.6

Factor $- 1$ out of $- (35 x) - 1 (- 3)$ .

$\frac{- (35 x - 3)}{10} = 1$

Step 1.4.7

Simplify the expression.

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Step 1.4.7.1

Rewrite $- (35 x - 3)$ as $- 1 (35 x - 3)$ .

$\frac{- 1 (35 x - 3)}{10} = 1$

Step 1.4.7.2

Move the negative in front of the fraction.

$- \frac{35 x - 3}{10} = 1$

Step 2

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

$- 10 (- \frac{35 x - 3}{10}) = - 10 \cdot 1$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 10 (- \frac{35 x - 3}{10})$ .

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Step 3.1.1.1

Cancel the common factor of $10$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{35 x - 3}{10}$ into the numerator.

$- 10 \frac{- (35 x - 3)}{10} = - 10 \cdot 1$

Step 3.1.1.1.2

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- (35 x - 3)}{10} = - 10 \cdot 1$

Step 3.1.1.1.3

Cancel the common factor.

$10 \cdot - 1 \frac{- (35 x - 3)}{10} = - 10 \cdot 1$

Step 3.1.1.1.4

Rewrite the expression.

$- - (35 x - 3) = - 10 \cdot 1$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (35 x - 3) = - 10 \cdot 1$

Step 3.1.1.2.2

Multiply $35 x - 3$ by $1$ .

$35 x - 3 = - 10 \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 10$ by $1$ .

$35 x - 3 = - 10$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$35 x = - 10 + 3$

Step 4.2

Add $- 10$ and $3$ .

$35 x = - 7$

Step 5

Divide each term in $35 x = - 7$ by $35$ and simplify.

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Step 5.1

Divide each term in $35 x = - 7$ by $35$ .

$\frac{35 x}{35} = \frac{- 7}{35}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $35$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{35 x}{35} = \frac{- 7}{35}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{35}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 7$ and $35$ .

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Step 5.3.1.1

Factor $7$ out of $- 7$ .

$x = \frac{7 (- 1)}{35}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $7$ out of $35$ .

$x = \frac{7 \cdot - 1}{7 \cdot 5}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{7 \cdot - 1}{7 \cdot 5}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{- 1}{5}$

Step 5.3.2

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{5}$

Decimal Form:

$x = - 0.2$