Pre-Algebra Examples

$3 - 2 x (x - 1) = x (3 - 2 x) - (x - 3)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x (3 - 2 x) - (x - 3) = 3 - 2 x (x - 1)$

Step 2

Simplify $x (3 - 2 x) - (x - 3)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x \cdot 3 + x (- 2 x) - (x - 3) = 3 - 2 x (x - 1)$

Step 2.1.2

Move $3$ to the left of $x$ .

$3 \cdot x + x (- 2 x) - (x - 3) = 3 - 2 x (x - 1)$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$3 \cdot x - 2 x \cdot x - (x - 3) = 3 - 2 x (x - 1)$

Step 2.1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.4.1

Move $x$ .

$3 x - 2 (x \cdot x) - (x - 3) = 3 - 2 x (x - 1)$

Step 2.1.4.2

Multiply $x$ by $x$ .

$3 x - 2 x^{2} - (x - 3) = 3 - 2 x (x - 1)$

Step 2.1.5

Apply the distributive property.

$3 x - 2 x^{2} - x - - 3 = 3 - 2 x (x - 1)$

Step 2.1.6

Multiply $- 1$ by $- 3$ .

$3 x - 2 x^{2} - x + 3 = 3 - 2 x (x - 1)$

Step 2.2

Subtract $x$ from $3 x$ .

$- 2 x^{2} + 2 x + 3 = 3 - 2 x (x - 1)$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $x$ by $x$ by adding the exponents.

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Step 3.2.1

Move $x$ .

$- 2 x^{2} + 2 x + 3 = 3 - 2 (x \cdot x) - 2 x \cdot - 1$

Step 3.2.2

Multiply $x$ by $x$ .

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

Step 3.3

Multiply $- 1$ by $- 2$ .

$- 2 x^{2} + 2 x + 3 = 3 - 2 x^{2} + 2 x$

Step 4

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

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Step 4.1

Add $2 x^{2}$ to both sides of the equation.

$- 2 x^{2} + 2 x + 3 + 2 x^{2} = 3 + 2 x$

Step 4.2

Subtract $2 x$ from both sides of the equation.

$- 2 x^{2} + 2 x + 3 + 2 x^{2} - 2 x = 3$

Step 4.3

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

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Step 4.3.1

Add $- 2 x^{2}$ and $2 x^{2}$ .

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

Step 4.3.2

Add $2 x + 3$ and $0$ .

$2 x + 3 - 2 x = 3$

Step 4.3.3

Subtract $2 x$ from $2 x$ .

$0 + 3 = 3$

Step 4.3.4

Add $0$ and $3$ .

$3 = 3$

Step 5

Since $3 = 3$ , the equation will always be true for any value of $x$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$