Basic Math Examples

$z - 5 = 7 z - 1 - z$

Step 1

Since $z$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$7 z - 1 - z = z - 5$

Step 2

Subtract $z$ from $7 z$ .

$6 z - 1 = z - 5$

Step 3

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

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Step 3.1

Subtract $z$ from both sides of the equation.

$6 z - 1 - z = - 5$

Step 3.2

Subtract $z$ from $6 z$ .

$5 z - 1 = - 5$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$5 z = - 5 + 1$

Step 4.2

Add $- 5$ and $1$ .

$5 z = - 4$

Step 5

Divide each term in $5 z = - 4$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 z = - 4$ by $5$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $z$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$z = - 0.8$