Basic Math Examples

$\frac{5 z - 3}{8} = z$

Step 1

Multiply both sides by $8$ .

$\frac{5 z - 3}{8} \cdot 8 = z \cdot 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $8$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{5 z - 3}{8} \cdot 8 = z \cdot 8$

Step 2.1.1.2

Rewrite the expression.

$5 z - 3 = z \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Move $8$ to the left of $z$ .

$5 z - 3 = 8 z$

Step 3

Solve for $z$ .

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Step 3.1

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

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Step 3.1.1

Subtract $8 z$ from both sides of the equation.

$5 z - 3 - 8 z = 0$

Step 3.1.2

Subtract $8 z$ from $5 z$ .

$- 3 z - 3 = 0$

Step 3.2

Add $3$ to both sides of the equation.

$- 3 z = 3$

Step 3.3

Divide each term in $- 3 z = 3$ by $- 3$ and simplify.

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Step 3.3.1

Divide each term in $- 3 z = 3$ by $- 3$ .

$\frac{- 3 z}{- 3} = \frac{3}{- 3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 3 z}{- 3} = \frac{3}{- 3}$

Step 3.3.2.1.2

Divide $z$ by $1$ .

$z = \frac{3}{- 3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $3$ by $- 3$ .

$z = - 1$