Pre-Algebra Examples

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

Step 1

Multiply both sides by $2$ .

$(\frac{x - 7}{5} + \frac{7}{5}) \cdot 2 = - \frac{x}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{x - 7}{5} + \frac{7}{5}) \cdot 2$ .

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Step 2.1.1.1

Combine the numerators over the common denominator.

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

Step 2.1.1.2

Combine the opposite terms in $x - 7 + 7$ .

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Step 2.1.1.2.1

Add $- 7$ and $7$ .

$\frac{x + 0}{5} \cdot 2 = - \frac{x}{2} \cdot 2$

Step 2.1.1.2.2

Add $x$ and $0$ .

$\frac{x}{5} \cdot 2 = - \frac{x}{2} \cdot 2$

Step 2.1.1.3

Combine $\frac{x}{5}$ and $2$ .

$\frac{x \cdot 2}{5} = - \frac{x}{2} \cdot 2$

Step 2.1.1.4

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

$\frac{2 x}{5} = - \frac{x}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

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

$\frac{2 x}{5} = \frac{- x}{2} \cdot 2$

Step 2.2.1.2

Cancel the common factor.

$\frac{2 x}{5} = \frac{- x}{2} \cdot 2$

Step 2.2.1.3

Rewrite the expression.

$\frac{2 x}{5} = - x$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $5$ .

$\frac{2 x}{5} \cdot 5 = - x \cdot 5$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{2 x}{5} \cdot 5 = - x \cdot 5$

Step 3.2.1.1.2

Rewrite the expression.

$2 x = - x \cdot 5$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $5$ by $- 1$ .

$2 x = - 5 x$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $5 x$ to both sides of the equation.

$2 x + 5 x = 0$

Step 3.3.1.2

Add $2 x$ and $5 x$ .

$7 x = 0$

Step 3.3.2

Divide each term in $7 x = 0$ by $7$ and simplify.

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Step 3.3.2.1

Divide each term in $7 x = 0$ by $7$ .

$\frac{7 x}{7} = \frac{0}{7}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{0}{7}$

Step 3.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{7}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Divide $0$ by $7$ .

$x = 0$