Algebra Examples

$2 e - 3 - \frac{1}{5} e = \frac{7}{5} + 3 e + 4$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{7}{5}$ from both sides of the equation.

$2 e - 3 - \frac{1}{5} e - \frac{7}{5} = 3 e + 4$

Step 1.2

Subtract $3 e$ from both sides of the equation.

$2 e - 3 - \frac{1}{5} e - \frac{7}{5} - 3 e = 4$

Step 1.3

Subtract $4$ from both sides of the equation.

$2 e - 3 - \frac{1}{5} e - \frac{7}{5} - 3 e - 4 = 0$

Step 2

Simplify $2 e - 3 - \frac{1}{5} e - \frac{7}{5} - 3 e - 4$ .

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Step 2.1

Combine $e$ and $\frac{1}{5}$ .

$2 e - 3 - \frac{e}{5} - \frac{7}{5} - 3 e - 4 = 0$

Step 2.2

To write $2 e$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 e \cdot \frac{5}{5} - \frac{e}{5} - 3 - \frac{7}{5} - 3 e - 4 = 0$

Step 2.3

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

$\frac{2 e \cdot 5}{5} - \frac{e}{5} - 3 - \frac{7}{5} - 3 e - 4 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 e \cdot 5 - e}{5} - 3 - \frac{7}{5} - 3 e - 4 = 0$

Step 2.5

Combine the numerators over the common denominator.

$- 3 - 3 e - 4 + \frac{2 e \cdot 5 - e - 7}{5} = 0$

Step 2.6

Multiply $5$ by $2$ .

$- 3 - 3 e - 4 + \frac{10 e - e - 7}{5} = 0$

Step 2.7

Subtract $e$ from $10 e$ .

$- 3 - 3 e - 4 + \frac{9 e - 7}{5} = 0$

Step 2.8

Subtract $4$ from $- 3$ .

$- 7 - 3 e + \frac{9 e - 7}{5} = 0$

Step 2.9

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 7 \cdot \frac{5}{5} + \frac{9 e - 7}{5} - 3 e = 0$

Step 2.10

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

$\frac{- 7 \cdot 5}{5} + \frac{9 e - 7}{5} - 3 e = 0$

Step 2.11

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 5 + 9 e - 7}{5} - 3 e = 0$

Step 2.12

Multiply $- 7$ by $5$ .

$\frac{- 35 + 9 e - 7}{5} - 3 e = 0$

Step 2.13

Subtract $7$ from $- 35$ .

$\frac{9 e - 42}{5} - 3 e = 0$

Step 2.14

To write $- 3 e$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9 e - 42}{5} - 3 e \cdot \frac{5}{5} = 0$

Step 2.15

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

$\frac{9 e - 42}{5} + \frac{- 3 e \cdot 5}{5} = 0$

Step 2.16

Combine the numerators over the common denominator.

$\frac{9 e - 42 - 3 e \cdot 5}{5} = 0$

Step 2.17

Simplify the numerator.

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Step 2.17.1

Multiply $5$ by $- 3$ .

$\frac{9 e - 42 - 15 e}{5} = 0$

Step 2.17.2

Subtract $15 e$ from $9 e$ .

$\frac{- 42 - 6 e}{5} = 0$

Step 2.18

Rewrite $- 42$ as $- 1 (42)$ .

$\frac{- 1 (42) - 6 e}{5} = 0$

Step 2.19

Factor $- 1$ out of $- 6 e$ .

$\frac{- 1 (42) - (6 e)}{5} = 0$

Step 2.20

Factor $- 1$ out of $- 1 (42) - (6 e)$ .

$\frac{- 1 (42 + 6 e)}{5} = 0$

Step 2.21

Move the negative in front of the fraction.

$- \frac{42 + 6 e}{5} = 0$

Step 3

Set the numerator equal to zero.

$42 + 6 e = 0$

Step 4

Solve the equation for .

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Step 4.1

Simplify $42 + 6 (2.71828182)$ .

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Step 4.1.1

Multiply $6$ by $2.71828182$ .

$42 + 16.30969097 = 0$

Step 4.1.2

Add $42$ and $16.30969097$ .

$58.30969097 = 0$

Step 4.2

Since $58.30969097 \neq 0$ , there are no solutions.

No solution