Algebra Examples

3 (x - 2) = 2 (2 x - 3)

$3 (x - 2) = 2 (2 x - 3)$

Step 1

Simplify

3 (x - 2)

$3 (x - 2)$ .

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Step 1.1

Rewrite.

0 + 0 + 3 (x - 2) = 2 (2 x - 3)

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

Step 1.2

Simplify by adding zeros.

3 (x - 2) = 2 (2 x - 3)

$3 (x - 2) = 2 (2 x - 3)$

Step 1.3

Apply the distributive property.

3 x + 3 \cdot - 2 = 2 (2 x - 3)

$3 x + 3 \cdot - 2 = 2 (2 x - 3)$

Step 1.4

Multiply

3

$3$ by

- 2

$- 2$ .

3 x - 6 = 2 (2 x - 3)

$3 x - 6 = 2 (2 x - 3)$

3 x - 6 = 2 (2 x - 3)

$3 x - 6 = 2 (2 x - 3)$

Step 2

Simplify

2 (2 x - 3)

$2 (2 x - 3)$ .

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Step 2.1

Apply the distributive property.

3 x - 6 = 2 (2 x) + 2 \cdot - 3

$3 x - 6 = 2 (2 x) + 2 \cdot - 3$

Step 2.2

Multiply.

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Step 2.2.1

Multiply

2

$2$ by

2

$2$ .

3 x - 6 = 4 x + 2 \cdot - 3

$3 x - 6 = 4 x + 2 \cdot - 3$

Step 2.2.2

Multiply

2

$2$ by

- 3

$- 3$ .

3 x - 6 = 4 x - 6

$3 x - 6 = 4 x - 6$

3 x - 6 = 4 x - 6

$3 x - 6 = 4 x - 6$

3 x - 6 = 4 x - 6

$3 x - 6 = 4 x - 6$

Step 3

Move all terms containing

x

$x$ to the left side of the equation.

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Step 3.1

Subtract

4 x

$4 x$ from both sides of the equation.

3 x - 6 - 4 x = - 6

$3 x - 6 - 4 x = - 6$

Step 3.2

Subtract

4 x

$4 x$ from

3 x

$3 x$ .

- x - 6 = - 6

$- x - 6 = - 6$

- x - 6 = - 6

$- x - 6 = - 6$

Step 4

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 4.1

Add

6

$6$ to both sides of the equation.

- x = - 6 + 6

$- x = - 6 + 6$

Step 4.2

Add

- 6

$- 6$ and

6

$6$ .

- x = 0

$- x = 0$

- x = 0

$- x = 0$

Step 5

Divide each term in

- x = 0

$- x = 0$ by

- 1

$- 1$ and simplify.

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Step 5.1

Divide each term in

- x = 0

$- x = 0$ by

- 1

$- 1$ .

\frac{- x}{- 1} = \frac{0}{- 1}

$\frac{- x}{- 1} = \frac{0}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

\frac{x}{1} = \frac{0}{- 1}

$\frac{x}{1} = \frac{0}{- 1}$

Step 5.2.2

Divide

x

$x$ by

1

$1$ .

x = \frac{0}{- 1}

$x = \frac{0}{- 1}$

x = \frac{0}{- 1}

$x = \frac{0}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide

0

$0$ by

- 1

$- 1$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

3 (x - 2) = 2 (2 x - 3)

$3 (x - 2) = 2 (2 x - 3)$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$