Finite Math Examples

$\frac{5 (x - 1)}{4} = x - 2$

Step 1

Multiply both sides by $4$ .

$\frac{5 (x - 1)}{4} \cdot 4 = (x - 2) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{5 (x - 1)}{4} \cdot 4 = (x - 2) \cdot 4$

Step 2.1.1.1.2

Rewrite the expression.

$5 (x - 1) = (x - 2) \cdot 4$

Step 2.1.1.2

Apply the distributive property.

$5 x + 5 \cdot - 1 = (x - 2) \cdot 4$

Step 2.1.1.3

Multiply $5$ by $- 1$ .

$5 x - 5 = (x - 2) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(x - 2) \cdot 4$ .

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Step 2.2.1.1

Apply the distributive property.

$5 x - 5 = x \cdot 4 - 2 \cdot 4$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $4$ to the left of $x$ .

$5 x - 5 = 4 \cdot x - 2 \cdot 4$

Step 2.2.1.2.2

Multiply $- 2$ by $4$ .

$5 x - 5 = 4 x - 8$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $4 x$ from both sides of the equation.

$5 x - 5 - 4 x = - 8$

Step 3.1.2

Subtract $4 x$ from $5 x$ .

$x - 5 = - 8$

Step 3.2

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

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Step 3.2.1

Add $5$ to both sides of the equation.

$x = - 8 + 5$

Step 3.2.2

Add $- 8$ and $5$ .

$x = - 3$