Algebra Examples

$2 d - e = 7$ $d + e = 5$

Step 1

Solve for $d$ in $2 d - e = 7$ .

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Step 1.1

Add $e$ to both sides of the equation.

$2 d = 7 + e$

$d + e = 5$

Step 1.2

Divide each term in $2 d = 7 + e$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 d = 7 + e$ by $2$ .

$\frac{2 d}{2} = \frac{7}{2} + \frac{e}{2}$

$d + e = 5$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 d}{2} = \frac{7}{2} + \frac{e}{2}$

$d + e = 5$

Step 1.2.2.1.2

Divide $d$ by $1$ .

$d = \frac{7}{2} + \frac{e}{2}$

$d + e = 5$

$d = \frac{7}{2} + \frac{e}{2}$

$d + e = 5$

$d = \frac{7}{2} + \frac{e}{2}$

$d + e = 5$

$d = \frac{7}{2} + \frac{e}{2}$

$d + e = 5$

$d = \frac{7}{2} + \frac{e}{2}$

$d + e = 5$

Step 2

Replace all occurrences of $d$ with $\frac{7}{2} + \frac{e}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $d$ in $d + e = 5$ with $\frac{7}{2} + \frac{e}{2}$ .

$(\frac{7}{2} + \frac{e}{2}) + e = 5$

$d = \frac{7}{2} + \frac{e}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $(\frac{7}{2} + \frac{e}{2}) + e$ .

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Step 2.2.1.1

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

$\frac{7}{2} + \frac{e}{2} + e \cdot \frac{2}{2} = 5$

$d = \frac{7}{2} + \frac{e}{2}$

Step 2.2.1.2

Combine fractions.

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Step 2.2.1.2.1

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

$\frac{7}{2} + \frac{e}{2} + \frac{e \cdot 2}{2} = 5$

$d = \frac{7}{2} + \frac{e}{2}$

Step 2.2.1.2.2

Combine the numerators over the common denominator.

$\frac{7}{2} + \frac{e + e \cdot 2}{2} = 5$

$d = \frac{7}{2} + \frac{e}{2}$

Step 2.2.1.2.3

Combine the numerators over the common denominator.

$\frac{7 + e + e \cdot 2}{2} = 5$

$d = \frac{7}{2} + \frac{e}{2}$

$\frac{7 + e + e \cdot 2}{2} = 5$

$d = \frac{7}{2} + \frac{e}{2}$

Step 2.2.1.3

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

$\frac{7 + e + 2 e}{2} = 5$

$d = \frac{7}{2} + \frac{e}{2}$

Step 2.2.1.4

Add $e$ and $2 e$ .

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

$d = \frac{7}{2} + \frac{e}{2}$

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

$d = \frac{7}{2} + \frac{e}{2}$

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

$d = \frac{7}{2} + \frac{e}{2}$

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

$d = \frac{7}{2} + \frac{e}{2}$

Step 3

Since $\frac{7 + 3 e}{2} = 5$ is not true, there is no solution.

No solution