Algebra Examples

$\frac{3}{5} e - 6 = - \frac{2}{5} (e - 10) - 7$

Step 1

Combine $\frac{3}{5}$ and $e$ .

$\frac{3 e}{5} - 6 = - \frac{2}{5} \cdot (e - 10) - 7$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{3 e}{5} - 6 = - \frac{2}{5} e - \frac{2}{5} \cdot - 10 - 7$

Step 2.2

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

$\frac{3 e}{5} - 6 = - \frac{e \cdot 2}{5} - \frac{2}{5} \cdot - 10 - 7$

Step 2.3

Cancel the common factor of $5$ .

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Step 2.3.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{3 e}{5} - 6 = - \frac{e \cdot 2}{5} + \frac{- 2}{5} \cdot - 10 - 7$

Step 2.3.2

Factor $5$ out of $- 10$ .

$\frac{3 e}{5} - 6 = - \frac{e \cdot 2}{5} + \frac{- 2}{5} \cdot (5 (- 2)) - 7$

Step 2.3.3

Cancel the common factor.

$\frac{3 e}{5} - 6 = - \frac{e \cdot 2}{5} + \frac{- 2}{5} \cdot (5 \cdot - 2) - 7$

Step 2.3.4

Rewrite the expression.

$\frac{3 e}{5} - 6 = - \frac{e \cdot 2}{5} - 2 \cdot - 2 - 7$

Step 2.4

Multiply $- 2$ by $- 2$ .

$\frac{3 e}{5} - 6 = - \frac{e \cdot 2}{5} + 4 - 7$

Step 2.5

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

$\frac{3 e}{5} - 6 = - \frac{2 e}{5} + 4 - 7$

Step 3

Subtract $7$ from $4$ .

$\frac{3 e}{5} - 6 = - \frac{2 e}{5} - 3$