Algebra Examples

$\frac{5}{8} e - 2 = 4 + \frac{1}{4} e - \frac{3}{4} e$

Step 1

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

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Step 1.1

Subtract $4$ from both sides of the equation.

$\frac{5}{8} e - 2 - 4 = \frac{1}{4} e - \frac{3}{4} e$

Step 1.2

Subtract $\frac{1}{4} e$ from both sides of the equation.

$\frac{5}{8} e - 2 - 4 - \frac{1}{4} e = - \frac{3}{4} e$

Step 1.3

Add $\frac{3}{4} e$ to both sides of the equation.

$\frac{5}{8} e - 2 - 4 - \frac{1}{4} e + \frac{3}{4} e = 0$

Step 2

Simplify $\frac{5}{8} e - 2 - 4 - \frac{1}{4} e + \frac{3}{4} e$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{5}{8}$ and $e$ .

$\frac{5 e}{8} - 2 - 4 - \frac{1}{4} e + \frac{3}{4} e = 0$

Step 2.1.2

Combine $e$ and $\frac{1}{4}$ .

$\frac{5 e}{8} - 2 - 4 - \frac{e}{4} + \frac{3}{4} e = 0$

Step 2.1.3

Combine $\frac{3}{4}$ and $e$ .

$\frac{5 e}{8} - 2 - 4 - \frac{e}{4} + \frac{3 e}{4} = 0$

Step 2.2

Combine the numerators over the common denominator.

$- 2 - 4 + \frac{5 e}{8} + \frac{- e + 3 e}{4} = 0$

Step 2.3

Add $- e$ and $3 e$ .

$- 2 - 4 + \frac{5 e}{8} + \frac{2 e}{4} = 0$

Step 2.4

Cancel the common factor of $2$ and $4$ .

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Step 2.4.1

Factor $2$ out of $2 e$ .

$- 2 - 4 + \frac{5 e}{8} + \frac{2 (e)}{4} = 0$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

$- 2 - 4 + \frac{5 e}{8} + \frac{2 e}{2 \cdot 2} = 0$

Step 2.4.2.2

Cancel the common factor.

$- 2 - 4 + \frac{5 e}{8} + \frac{2 e}{2 \cdot 2} = 0$

Step 2.4.2.3

Rewrite the expression.

$- 2 - 4 + \frac{5 e}{8} + \frac{e}{2} = 0$

Step 2.5

Subtract $4$ from $- 2$ .

$- 6 + \frac{5 e}{8} + \frac{e}{2} = 0$

Step 2.6

To write $\frac{e}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 6 + \frac{5 e}{8} + \frac{e}{2} \cdot \frac{4}{4} = 0$

Step 2.7

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.7.1

Multiply $\frac{e}{2}$ by $\frac{4}{4}$ .

$- 6 + \frac{5 e}{8} + \frac{e \cdot 4}{2 \cdot 4} = 0$

Step 2.7.2

Multiply $2$ by $4$ .

$- 6 + \frac{5 e}{8} + \frac{e \cdot 4}{8} = 0$

Step 2.8

Combine the numerators over the common denominator.

$- 6 + \frac{5 e + e \cdot 4}{8} = 0$

Step 2.9

Add $5 e$ and $e \cdot 4$ .

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Step 2.9.1

Reorder $e$ and $4$ .

$- 6 + \frac{5 e + 4 \cdot e}{8} = 0$

Step 2.9.2

Add $5 e$ and $4 \cdot e$ .

$- 6 + \frac{9 e}{8} = 0$

Step 3

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- 6 \cdot \frac{8}{8} + \frac{9 e}{8} = 0$

Step 4

Combine $- 6$ and $\frac{8}{8}$ .

$\frac{- 6 \cdot 8}{8} + \frac{9 e}{8} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{- 6 \cdot 8 + 9 e}{8} = 0$

Step 6

Multiply $- 6$ by $8$ .

$\frac{- 48 + 9 e}{8} = 0$

Step 7

Set the numerator equal to zero.

$- 48 + 9 e = 0$

Step 8

Solve the equation for .

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Step 8.1

Simplify $- 48 + 9 (2.71828182)$ .

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Step 8.1.1

Multiply $9$ by $2.71828182$ .

$- 48 + 24.46453645 = 0$

Step 8.1.2

Add $- 48$ and $24.46453645$ .

$- 23.53546354 = 0$

Step 8.2

Since $- 23.53546354 \neq 0$ , there are no solutions.

No solution