Algebra Examples

$- 5 (x + 10) \frac{7}{2} = - 390$ , $625$

Simplify.

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Combine $\frac{7}{2}$ and $- 5$ .

$\frac{7 \cdot - 5}{2} (x + 10) = - 390$

Multiply $7$ by $- 5$ .

$\frac{- 35}{2} (x + 10) = - 390$

Multiply each term in $\frac{- 35}{2} \cdot (x + 10) = - 390$ by $- \frac{2}{35}$ to eliminate the fractions.

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Multiply each term in $\frac{- 35}{2} \cdot (x + 10) = - 390$ by $- \frac{2}{35}$ .

$\frac{- 35}{2} \cdot (x + 10) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Simplify the left side.

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Simplify terms.

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Move the negative in front of the fraction.

$- \frac{35}{2} \cdot (x + 10) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Apply the distributive property.

$(- \frac{35}{2} x - \frac{35}{2} \cdot 10) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Combine $x$ and $\frac{35}{2}$ .

$(- \frac{x \cdot 35}{2} - \frac{35}{2} \cdot 10) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{35}{2}$ into the numerator.

$(- \frac{x \cdot 35}{2} + \frac{- 35}{2} \cdot 10) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Factor $2$ out of $10$ .

$(- \frac{x \cdot 35}{2} + \frac{- 35}{2} \cdot (2 (5))) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Cancel the common factor.

$(- \frac{x \cdot 35}{2} + \frac{- 35}{2} \cdot (2 \cdot 5)) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Rewrite the expression.

$(- \frac{x \cdot 35}{2} - 35 \cdot 5) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Multiply $- 35$ by $5$ .

$(- \frac{x \cdot 35}{2} - 175) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Move $35$ to the left of $x$ .

$(- \frac{35 x}{2} - 175) (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Simplify terms.

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Apply the distributive property.

$- \frac{35 x}{2} (- \frac{2}{35}) - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Cancel the common factor of $35$ .

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Move the leading negative in $- \frac{35 x}{2}$ into the numerator.

$\frac{- 35 x}{2} (- \frac{2}{35}) - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Move the leading negative in $- \frac{2}{35}$ into the numerator.

$\frac{- 35 x}{2} \cdot \frac{- 2}{35} - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Factor $35$ out of $- 35 x$ .

$\frac{35 (- x)}{2} \cdot \frac{- 2}{35} - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Cancel the common factor.

$\frac{35 (- x)}{2} \cdot \frac{- 2}{35} - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Rewrite the expression.

$\frac{- x}{2} \cdot - 2 - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Cancel the common factor of $2$ .

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Factor $2$ out of $- 2$ .

$\frac{- x}{2} \cdot (2 (- 1)) - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Cancel the common factor.

$\frac{- x}{2} \cdot (2 \cdot - 1) - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Rewrite the expression.

$- x \cdot - 1 - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 x - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Multiply $x$ by $1$ .

$x - 175 (- \frac{2}{35}) = - 390 (- \frac{2}{35})$

Cancel the common factor of $35$ .

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Move the leading negative in $- \frac{2}{35}$ into the numerator.

$x - 175 (\frac{- 2}{35}) = - 390 (- \frac{2}{35})$

Factor $35$ out of $- 175$ .

$x + 35 (- 5) \frac{- 2}{35} = - 390 (- \frac{2}{35})$

Cancel the common factor.

$x + 35 \cdot - 5 \frac{- 2}{35} = - 390 (- \frac{2}{35})$

Rewrite the expression.

$x - 5 \cdot - 2 = - 390 (- \frac{2}{35})$

Multiply $- 5$ by $- 2$ .

$x + 10 = - 390 (- \frac{2}{35})$

Simplify the right side.

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Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{2}{35}$ into the numerator.

$x + 10 = - 390 (\frac{- 2}{35})$

Factor $5$ out of $- 390$ .

$x + 10 = 5 (- 78) \frac{- 2}{35}$

Factor $5$ out of $35$ .

$x + 10 = 5 \cdot - 78 \frac{- 2}{5 \cdot 7}$

Cancel the common factor.

$x + 10 = 5 \cdot - 78 \frac{- 2}{5 \cdot 7}$

Rewrite the expression.

$x + 10 = - 78 (\frac{- 2}{7})$

Combine $- 78$ and $\frac{- 2}{7}$ .

$x + 10 = \frac{- 78 \cdot - 2}{7}$

Multiply $- 78$ by $- 2$ .

$x + 10 = \frac{156}{7}$

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

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Subtract $10$ from both sides of the equation.

$x = \frac{156}{7} - 10$

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = \frac{156}{7} - 10 \cdot \frac{7}{7}$

Combine $- 10$ and $\frac{7}{7}$ .

$x = \frac{156}{7} + \frac{- 10 \cdot 7}{7}$

Combine the numerators over the common denominator.

$x = \frac{156 - 10 \cdot 7}{7}$

Simplify the numerator.

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Multiply $- 10$ by $7$ .

$x = \frac{156 - 70}{7}$

Subtract $70$ from $156$ .

$x = \frac{86}{7}$

Replace the variable $x$ with $\frac{86}{7}$ in the expression.

$625$