Basic Math Examples

$2 z - \frac{7}{5} = - \frac{7}{2} z - \frac{3}{5}$

Step 1

Simplify each term.

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Step 1.1

Combine $z$ and $\frac{7}{2}$ .

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

Step 1.2

Move $7$ to the left of $z$ .

$2 z - \frac{7}{5} = - \frac{7 z}{2} - \frac{3}{5}$

Step 2

Move all terms containing $z$ to the left side of the equation.

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Step 2.1

Add $\frac{7 z}{2}$ to both sides of the equation.

$2 z - \frac{7}{5} + \frac{7 z}{2} = - \frac{3}{5}$

Step 2.2

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

$2 z \cdot \frac{2}{2} + \frac{7 z}{2} - \frac{7}{5} = - \frac{3}{5}$

Step 2.3

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

$\frac{2 z \cdot 2}{2} + \frac{7 z}{2} - \frac{7}{5} = - \frac{3}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 z \cdot 2 + 7 z}{2} - \frac{7}{5} = - \frac{3}{5}$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $z$ out of $2 z \cdot 2 + 7 z$ .

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Step 2.5.1.1.1

Factor $z$ out of $2 z \cdot 2$ .

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

Step 2.5.1.1.2

Factor $z$ out of $7 z$ .

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

Step 2.5.1.1.3

Factor $z$ out of $z (2 \cdot 2) + z \cdot 7$ .

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

Step 2.5.1.2

Multiply $2$ by $2$ .

$\frac{z (4 + 7)}{2} - \frac{7}{5} = - \frac{3}{5}$

Step 2.5.1.3

Add $4$ and $7$ .

$\frac{z \cdot 11}{2} - \frac{7}{5} = - \frac{3}{5}$

Step 2.5.2

Move $11$ to the left of $z$ .

$\frac{11 z}{2} - \frac{7}{5} = - \frac{3}{5}$

Step 3

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

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Step 3.1

Add $\frac{7}{5}$ to both sides of the equation.

$\frac{11 z}{2} = - \frac{3}{5} + \frac{7}{5}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{11 z}{2} = \frac{- 3 + 7}{5}$

Step 3.3

Add $- 3$ and $7$ .

$\frac{11 z}{2} = \frac{4}{5}$

Step 4

Multiply both sides of the equation by $\frac{2}{11}$ .

$\frac{2}{11} \cdot \frac{11 z}{2} = \frac{2}{11} \cdot \frac{4}{5}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{2}{11} \cdot \frac{11 z}{2}$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{2}{11} \cdot \frac{11 z}{2} = \frac{2}{11} \cdot \frac{4}{5}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 z) = \frac{2}{11} \cdot \frac{4}{5}$

Step 5.1.1.2

Cancel the common factor of $11$ .

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Step 5.1.1.2.1

Factor $11$ out of $11 z$ .

$\frac{1}{11} (11 (z)) = \frac{2}{11} \cdot \frac{4}{5}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 z) = \frac{2}{11} \cdot \frac{4}{5}$

Step 5.1.1.2.3

Rewrite the expression.

$z = \frac{2}{11} \cdot \frac{4}{5}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{2}{11} \cdot \frac{4}{5}$ .

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Step 5.2.1.1

Multiply $\frac{2}{11}$ by $\frac{4}{5}$ .

$z = \frac{2 \cdot 4}{11 \cdot 5}$

Step 5.2.1.2

Multiply $2$ by $4$ .

$z = \frac{8}{11 \cdot 5}$

Step 5.2.1.3

Multiply $11$ by $5$ .

$z = \frac{8}{55}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = \frac{8}{55}$

Decimal Form:

$z = 0.1\overline{45}$