Algebra Examples

$\frac{7 - 2 x}{6} = \frac{x - 5}{1}$

Step 1

Multiply both sides by $6$ .

$\frac{7 - 2 x}{6} \cdot 6 = \frac{x - 5}{1} \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{7 - 2 x}{6} \cdot 6$ .

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Step 2.1.1.1

Cancel the common factor of $6$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{7 - 2 x}{6} \cdot 6 = \frac{x - 5}{1} \cdot 6$

Step 2.1.1.1.2

Rewrite the expression.

$7 - 2 x = \frac{x - 5}{1} \cdot 6$

Step 2.1.1.2

Reorder $7$ and $- 2 x$ .

$- 2 x + 7 = \frac{x - 5}{1} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{x - 5}{1} \cdot 6$ .

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Step 2.2.1.1

Divide $x - 5$ by $1$ .

$- 2 x + 7 = (x - 5) \cdot 6$

Step 2.2.1.2

Apply the distributive property.

$- 2 x + 7 = x \cdot 6 - 5 \cdot 6$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Move $6$ to the left of $x$ .

$- 2 x + 7 = 6 \cdot x - 5 \cdot 6$

Step 2.2.1.3.2

Multiply $- 5$ by $6$ .

$- 2 x + 7 = 6 x - 30$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $6 x$ from both sides of the equation.

$- 2 x + 7 - 6 x = - 30$

Step 3.1.2

Subtract $6 x$ from $- 2 x$ .

$- 8 x + 7 = - 30$

Step 3.2

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

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Step 3.2.1

Subtract $7$ from both sides of the equation.

$- 8 x = - 30 - 7$

Step 3.2.2

Subtract $7$ from $- 30$ .

$- 8 x = - 37$

Step 3.3

Divide each term in $- 8 x = - 37$ by $- 8$ and simplify.

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Step 3.3.1

Divide each term in $- 8 x = - 37$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 37}{- 8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 37}{- 8}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 37}{- 8}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{37}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{37}{8}$

Decimal Form:

$x = 4.625$

Mixed Number Form:

$x = 4 \frac{5}{8}$