Pre-Algebra Examples

$3 (x - 1) = 5 x - 6$

Step 1

Simplify $3 (x - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (x - 1) = 5 x - 6$

Step 1.2

Simplify by adding zeros.

$3 (x - 1) = 5 x - 6$

Step 1.3

Apply the distributive property.

$3 x + 3 \cdot - 1 = 5 x - 6$

Step 1.4

Multiply $3$ by $- 1$ .

$3 x - 3 = 5 x - 6$

Step 2

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

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Step 2.1

Subtract $5 x$ from both sides of the equation.

$3 x - 3 - 5 x = - 6$

Step 2.2

Subtract $5 x$ from $3 x$ .

$- 2 x - 3 = - 6$

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

$- 2 x = - 6 + 3$

Step 3.2

Add $- 6$ and $3$ .

$- 2 x = - 3$

Step 4

Divide each term in $- 2 x = - 3$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x = - 3$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 3}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 3}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$x = \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$