Basic Math Examples

$7 z + 4 (z - 2) - z = 5 z - 2 (z - 4 (- z))$

Step 1

Simplify $7 z + 4 (z - 2) - z$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$7 z + 4 z + 4 \cdot - 2 - z = 5 z - 2 (z - 4 (- z))$

Step 1.1.2

Multiply $4$ by $- 2$ .

$7 z + 4 z - 8 - z = 5 z - 2 (z - 4 (- z))$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $7 z$ and $4 z$ .

$11 z - 8 - z = 5 z - 2 (z - 4 (- z))$

Step 1.2.2

Subtract $z$ from $11 z$ .

$10 z - 8 = 5 z - 2 (z - 4 (- z))$

Step 2

Simplify $5 z - 2 (z - 4 (- z))$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 1$ by $- 4$ .

$10 z - 8 = 5 z - 2 (z + 4 z)$

Step 2.1.2

Add $z$ and $4 z$ .

$10 z - 8 = 5 z - 2 (5 z)$

Step 2.1.3

Multiply $5$ by $- 2$ .

$10 z - 8 = 5 z - 10 z$

Step 2.2

Subtract $10 z$ from $5 z$ .

$10 z - 8 = - 5 z$

Step 3

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

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Step 3.1

Add $5 z$ to both sides of the equation.

$10 z - 8 + 5 z = 0$

Step 3.2

Add $10 z$ and $5 z$ .

$15 z - 8 = 0$

Step 4

Add $8$ to both sides of the equation.

$15 z = 8$

Step 5

Divide each term in $15 z = 8$ by $15$ and simplify.

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Step 5.1

Divide each term in $15 z = 8$ by $15$ .

$\frac{15 z}{15} = \frac{8}{15}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $15$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{15 z}{15} = \frac{8}{15}$

Step 5.2.1.2

Divide $z$ by $1$ .

$z = \frac{8}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = \frac{8}{15}$

Decimal Form:

$z = 0.5\overline{3}$