Algebra Examples

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

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

Step 1

Multiply both sides by

2

$2$ .

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

$2$ .

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Step 2.1.1.1

Cancel the common factor.

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

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

Step 2.1.1.2

Rewrite the expression.

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

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

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

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

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

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify

(x - 71) \cdot 2

$(x - 71) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

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

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

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move

2

$2$ to the left of

x

$x$ .

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

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

Step 2.2.1.2.2

Multiply

- 71

$- 71$ by

2

$2$ .

x + 51 = 2 x - 142

$x + 51 = 2 x - 142$

x + 51 = 2 x - 142

$x + 51 = 2 x - 142$

x + 51 = 2 x - 142

$x + 51 = 2 x - 142$

x + 51 = 2 x - 142

$x + 51 = 2 x - 142$

x + 51 = 2 x - 142

$x + 51 = 2 x - 142$

Step 3

Solve for

x

$x$ .

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Step 3.1

Move all terms containing

x

$x$ to the left side of the equation.

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Step 3.1.1

Subtract

2 x

$2 x$ from both sides of the equation.

x + 51 - 2 x = - 142

$x + 51 - 2 x = - 142$

Step 3.1.2

Subtract

2 x

$2 x$ from

x

$x$ .

- x + 51 = - 142

$- x + 51 = - 142$

- x + 51 = - 142

$- x + 51 = - 142$

Step 3.2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 3.2.1

Subtract

51

$51$ from both sides of the equation.

- x = - 142 - 51

$- x = - 142 - 51$

Step 3.2.2

Subtract

51

$51$ from

- 142

$- 142$ .

- x = - 193

$- x = - 193$

- x = - 193

$- x = - 193$

Step 3.3

Divide each term in

- x = - 193

$- x = - 193$ by

- 1

$- 1$ and simplify.

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Step 3.3.1

Divide each term in

- x = - 193

$- x = - 193$ by

- 1

$- 1$ .

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

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

Step 3.3.2.2

Divide

x

$x$ by

1

$1$ .

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

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

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

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide

- 193

$- 193$ by

- 1

$- 1$ .

x = 193

$x = 193$

x = 193

$x = 193$

x = 193

$x = 193$

x = 193

$x = 193$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$