Basic Math Examples

$\frac{7 z - 8}{2 z - 2} = \frac{3}{1}$

Step 1

Factor each term.

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Step 1.1

Factor $2$ out of $2 z - 2$ .

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Step 1.1.1

Factor $2$ out of $2 z$ .

$\frac{7 z - 8}{2 (z) - 2} = \frac{3}{1}$

Step 1.1.2

Factor $2$ out of $- 2$ .

$\frac{7 z - 8}{2 (z) + 2 (- 1)} = \frac{3}{1}$

Step 1.1.3

Factor $2$ out of $2 (z) + 2 (- 1)$ .

$\frac{7 z - 8}{2 (z - 1)} = \frac{3}{1}$

Step 1.2

Divide $3$ by $1$ .

$\frac{7 z - 8}{2 (z - 1)} = 3$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 (z - 1), 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 (z - 1)$

Step 3

Multiply each term in $\frac{7 z - 8}{2 (z - 1)} = 3$ by $2 (z - 1)$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{7 z - 8}{2 (z - 1)} = 3$ by $2 (z - 1)$ .

$\frac{7 z - 8}{2 (z - 1)} (2 (z - 1)) = 3 (2 (z - 1))$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{7 z - 8}{2 (z - 1)} (z - 1) = 3 (2 (z - 1))$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Cancel the common factor.

$2 \frac{7 z - 8}{2 (z - 1)} (z - 1) = 3 (2 (z - 1))$

Step 3.2.2.2

Rewrite the expression.

$\frac{7 z - 8}{z - 1} (z - 1) = 3 (2 (z - 1))$

Step 3.2.3

Cancel the common factor of $z - 1$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{7 z - 8}{z - 1} (z - 1) = 3 (2 (z - 1))$

Step 3.2.3.2

Rewrite the expression.

$7 z - 8 = 3 (2 (z - 1))$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$7 z - 8 = 3 (2 z + 2 \cdot - 1)$

Step 3.3.2

Multiply $2$ by $- 1$ .

$7 z - 8 = 3 (2 z - 2)$

Step 3.3.3

Apply the distributive property.

$7 z - 8 = 3 (2 z) + 3 \cdot - 2$

Step 3.3.4

Multiply.

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Step 3.3.4.1

Multiply $2$ by $3$ .

$7 z - 8 = 6 z + 3 \cdot - 2$

Step 3.3.4.2

Multiply $3$ by $- 2$ .

$7 z - 8 = 6 z - 6$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

Subtract $6 z$ from both sides of the equation.

$7 z - 8 - 6 z = - 6$

Step 4.1.2

Subtract $6 z$ from $7 z$ .

$z - 8 = - 6$

Step 4.2

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

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Step 4.2.1

Add $8$ to both sides of the equation.

$z = - 6 + 8$

Step 4.2.2

Add $- 6$ and $8$ .

$z = 2$