Basic Math Examples

$\frac{6}{5} \cdot (5 z - 1) - 4 z = \frac{7}{5}$

Step 1

Simplify $\frac{6}{5} \cdot (5 z - 1) - 4 z$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{6}{5} (5 z) + \frac{6}{5} \cdot - 1 - 4 z = \frac{7}{5}$

Step 1.1.2

Cancel the common factor of $5$ .

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Step 1.1.2.1

Factor $5$ out of $5 z$ .

$\frac{6}{5} (5 (z)) + \frac{6}{5} \cdot - 1 - 4 z = \frac{7}{5}$

Step 1.1.2.2

Cancel the common factor.

$\frac{6}{5} (5 z) + \frac{6}{5} \cdot - 1 - 4 z = \frac{7}{5}$

Step 1.1.2.3

Rewrite the expression.

$6 z + \frac{6}{5} \cdot - 1 - 4 z = \frac{7}{5}$

Step 1.1.3

Multiply $\frac{6}{5} \cdot - 1$ .

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Step 1.1.3.1

Combine $\frac{6}{5}$ and $- 1$ .

$6 z + \frac{6 \cdot - 1}{5} - 4 z = \frac{7}{5}$

Step 1.1.3.2

Multiply $6$ by $- 1$ .

$6 z + \frac{- 6}{5} - 4 z = \frac{7}{5}$

Step 1.1.4

Move the negative in front of the fraction.

$6 z - \frac{6}{5} - 4 z = \frac{7}{5}$

Step 1.2

Subtract $4 z$ from $6 z$ .

$2 z - \frac{6}{5} = \frac{7}{5}$

Step 2

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

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Step 2.1

Add $\frac{6}{5}$ to both sides of the equation.

$2 z = \frac{7}{5} + \frac{6}{5}$

Step 2.2

Combine the numerators over the common denominator.

$2 z = \frac{7 + 6}{5}$

Step 2.3

Add $7$ and $6$ .

$2 z = \frac{13}{5}$

Step 3

Divide each term in $2 z = \frac{13}{5}$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 z = \frac{13}{5}$ by $2$ .

$\frac{2 z}{2} = \frac{\frac{13}{5}}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 z}{2} = \frac{\frac{13}{5}}{2}$

Step 3.2.1.2

Divide $z$ by $1$ .

$z = \frac{\frac{13}{5}}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$z = \frac{13}{5} \cdot \frac{1}{2}$

Step 3.3.2

Multiply $\frac{13}{5} \cdot \frac{1}{2}$ .

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Step 3.3.2.1

Multiply $\frac{13}{5}$ by $\frac{1}{2}$ .

$z = \frac{13}{5 \cdot 2}$

Step 3.3.2.2

Multiply $5$ by $2$ .

$z = \frac{13}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{13}{10}$

Decimal Form:

$z = 1.3$

Mixed Number Form:

$z = 1 \frac{3}{10}$