Algebra Examples

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

Step 1

Subtract $3 (x - \frac{2}{3})$ from both sides of the equation.

$3 x - 2 - 3 (x - \frac{2}{3}) = 0$

Step 2

Simplify $3 x - 2 - 3 (x - \frac{2}{3})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 x - 2 - 3 x - 3 (- \frac{2}{3}) = 0$

Step 2.1.2

Cancel the common factor of $3$ .

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Step 2.1.2.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$3 x - 2 - 3 x - 3 (\frac{- 2}{3}) = 0$

Step 2.1.2.2

Factor $3$ out of $- 3$ .

$3 x - 2 - 3 x + 3 (- 1) \frac{- 2}{3} = 0$

Step 2.1.2.3

Cancel the common factor.

$3 x - 2 - 3 x + 3 \cdot - 1 \frac{- 2}{3} = 0$

Step 2.1.2.4

Rewrite the expression.

$3 x - 2 - 3 x - 1 \cdot - 2 = 0$

Step 2.1.3

Multiply $- 1$ by $- 2$ .

$3 x - 2 - 3 x + 2 = 0$

Step 2.2

Combine the opposite terms in $3 x - 2 - 3 x + 2$ .

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Step 2.2.1

Subtract $3 x$ from $3 x$ .

$0 - 2 + 2 = 0$

Step 2.2.2

Subtract $2$ from $0$ .

$- 2 + 2 = 0$

Step 2.2.3

Add $- 2$ and $2$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true