Algebra Examples

$4 - (7 x + 7) = \frac{3}{2} (- 9 x + \frac{2}{3}) + x$

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.

$\frac{3}{2} \cdot (- 9 x + \frac{2}{3}) + x = 4 - (7 x + 7)$

Step 2

Simplify $\frac{3}{2} \cdot (- 9 x + \frac{2}{3}) + x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{3}{2} (- 9 x) + \frac{3}{2} \cdot \frac{2}{3} + x = 4 - (7 x + 7)$

Step 2.1.2

Multiply $\frac{3}{2} (- 9 x)$ .

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Step 2.1.2.1

Combine $- 9$ and $\frac{3}{2}$ .

$\frac{- 9 \cdot 3}{2} x + \frac{3}{2} \cdot \frac{2}{3} + x = 4 - (7 x + 7)$

Step 2.1.2.2

Multiply $- 9$ by $3$ .

$\frac{- 27}{2} x + \frac{3}{2} \cdot \frac{2}{3} + x = 4 - (7 x + 7)$

Step 2.1.2.3

Combine $\frac{- 27}{2}$ and $x$ .

$\frac{- 27 x}{2} + \frac{3}{2} \cdot \frac{2}{3} + x = 4 - (7 x + 7)$

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Cancel the common factor.

$\frac{- 27 x}{2} + \frac{3}{2} \cdot \frac{2}{3} + x = 4 - (7 x + 7)$

Step 2.1.3.2

Rewrite the expression.

$\frac{- 27 x}{2} + \frac{1}{2} \cdot 2 + x = 4 - (7 x + 7)$

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Cancel the common factor.

$\frac{- 27 x}{2} + \frac{1}{2} \cdot 2 + x = 4 - (7 x + 7)$

Step 2.1.4.2

Rewrite the expression.

$\frac{- 27 x}{2} + 1 + x = 4 - (7 x + 7)$

Step 2.1.5

Move the negative in front of the fraction.

$- \frac{27 x}{2} + 1 + x = 4 - (7 x + 7)$

Step 2.2

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

$- \frac{27 x}{2} + x \cdot \frac{2}{2} + 1 = 4 - (7 x + 7)$

Step 2.3

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

$- \frac{27 x}{2} + \frac{x \cdot 2}{2} + 1 = 4 - (7 x + 7)$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 27 x + x \cdot 2}{2} + 1 = 4 - (7 x + 7)$

Step 2.5

Add $- 27 x$ and $x \cdot 2$ .

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Step 2.5.1

Reorder $x$ and $2$ .

$\frac{- 27 x + 2 \cdot x}{2} + 1 = 4 - (7 x + 7)$

Step 2.5.2

Add $- 27 x$ and $2 \cdot x$ .

$\frac{- 25 x}{2} + 1 = 4 - (7 x + 7)$

Step 2.6

Move the negative in front of the fraction.

$- \frac{25 x}{2} + 1 = 4 - (7 x + 7)$

Step 3

Simplify $4 - (7 x + 7)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- \frac{25 x}{2} + 1 = 4 - (7 x) - 1 \cdot 7$

Step 3.1.2

Multiply $7$ by $- 1$ .

$- \frac{25 x}{2} + 1 = 4 - 7 x - 1 \cdot 7$

Step 3.1.3

Multiply $- 1$ by $7$ .

$- \frac{25 x}{2} + 1 = 4 - 7 x - 7$

Step 3.2

Subtract $7$ from $4$ .

$- \frac{25 x}{2} + 1 = - 7 x - 3$

Step 4

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

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Step 4.1

Add $7 x$ to both sides of the equation.

$- \frac{25 x}{2} + 1 + 7 x = - 3$

Step 4.2

To write $7 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{25 x}{2} + 7 x \cdot \frac{2}{2} + 1 = - 3$

Step 4.3

Combine $7 x$ and $\frac{2}{2}$ .

$- \frac{25 x}{2} + \frac{7 x \cdot 2}{2} + 1 = - 3$

Step 4.4

Combine the numerators over the common denominator.

$\frac{- 25 x + 7 x \cdot 2}{2} + 1 = - 3$

Step 4.5

Simplify each term.

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Step 4.5.1

Simplify the numerator.

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Step 4.5.1.1

Factor $x$ out of $- 25 x + 7 x \cdot 2$ .

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Step 4.5.1.1.1

Factor $x$ out of $- 25 x$ .

$\frac{x \cdot - 25 + 7 x \cdot 2}{2} + 1 = - 3$

Step 4.5.1.1.2

Factor $x$ out of $7 x \cdot 2$ .

$\frac{x \cdot - 25 + x (7 \cdot 2)}{2} + 1 = - 3$

Step 4.5.1.1.3

Factor $x$ out of $x \cdot - 25 + x (7 \cdot 2)$ .

$\frac{x (- 25 + 7 \cdot 2)}{2} + 1 = - 3$

Step 4.5.1.2

Multiply $7$ by $2$ .

$\frac{x (- 25 + 14)}{2} + 1 = - 3$

Step 4.5.1.3

Add $- 25$ and $14$ .

$\frac{x \cdot - 11}{2} + 1 = - 3$

Step 4.5.2

Move $- 11$ to the left of $x$ .

$\frac{- 11 \cdot x}{2} + 1 = - 3$

Step 4.5.3

Move the negative in front of the fraction.

$- \frac{11 x}{2} + 1 = - 3$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$- \frac{11 x}{2} = - 3 - 1$

Step 5.2

Subtract $1$ from $- 3$ .

$- \frac{11 x}{2} = - 4$

Step 6

Multiply both sides of the equation by $- \frac{2}{11}$ .

$- \frac{2}{11} (- \frac{11 x}{2}) = - \frac{2}{11} \cdot - 4$

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify $- \frac{2}{11} (- \frac{11 x}{2})$ .

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Step 7.1.1.1

Cancel the common factor of $2$ .

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Step 7.1.1.1.1

Move the leading negative in $- \frac{2}{11}$ into the numerator.

$\frac{- 2}{11} (- \frac{11 x}{2}) = - \frac{2}{11} \cdot - 4$

Step 7.1.1.1.2

Move the leading negative in $- \frac{11 x}{2}$ into the numerator.

$\frac{- 2}{11} \cdot \frac{- 11 x}{2} = - \frac{2}{11} \cdot - 4$

Step 7.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{11} \cdot \frac{- 11 x}{2} = - \frac{2}{11} \cdot - 4$

Step 7.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{11} \cdot \frac{- 11 x}{2} = - \frac{2}{11} \cdot - 4$

Step 7.1.1.1.5

Rewrite the expression.

$\frac{- 1}{11} (- 11 x) = - \frac{2}{11} \cdot - 4$

Step 7.1.1.2

Cancel the common factor of $11$ .

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Step 7.1.1.2.1

Factor $11$ out of $- 11 x$ .

$\frac{- 1}{11} (11 (- x)) = - \frac{2}{11} \cdot - 4$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{- 1}{11} (11 (- x)) = - \frac{2}{11} \cdot - 4$

Step 7.1.1.2.3

Rewrite the expression.

$- - x = - \frac{2}{11} \cdot - 4$

Step 7.1.1.3

Multiply.

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Step 7.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{11} \cdot - 4$

Step 7.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{2}{11} \cdot - 4$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $- \frac{2}{11} \cdot - 4$ .

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Step 7.2.1.1

Multiply $- 4$ by $- 1$ .

$x = 4 (\frac{2}{11})$

Step 7.2.1.2

Combine $4$ and $\frac{2}{11}$ .

$x = \frac{4 \cdot 2}{11}$

Step 7.2.1.3

Multiply $4$ by $2$ .

$x = \frac{8}{11}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{11}$

Decimal Form:

$x = 0.\overline{72}$