Algebra Examples

$\frac{x + 51}{2} = x - 71$

Step 1

Multiply both sides by $2$ .

$\frac{x + 51}{2} \cdot 2 = (x - 71) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x + 51}{2} \cdot 2 = (x - 71) \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$x + 51 = (x - 71) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(x - 71) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$x + 51 = x \cdot 2 - 71 \cdot 2$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $2$ to the left of $x$ .

$x + 51 = 2 \cdot x - 71 \cdot 2$

Step 2.2.1.2.2

Multiply $- 71$ by $2$ .

$x + 51 = 2 x - 142$

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 $2 x$ from both sides of the equation.

$x + 51 - 2 x = - 142$

Step 3.1.2

Subtract $2 x$ from $x$ .

$- x + 51 = - 142$

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 $51$ from both sides of the equation.

$- x = - 142 - 51$

Step 3.2.2

Subtract $51$ from $- 142$ .

$- x = - 193$

Step 3.3

Divide each term in $- x = - 193$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- x = - 193$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 193}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 193}{- 1}$

Step 3.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 193}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 193$ by $- 1$ .

$x = 193$