Convert to Set Notation 4x(x-2)<2(2x-1)(x-3)

$4 x (x - 2) < 2 (2 x - 1) (x - 3)$

Solve $x < 1$ .

Simplify $4 x (x - 2)$ .

Start simplifying.

$0 + 0 + 4 x (x - 2) < 2 (2 x - 1) (x - 3)$

Simplify by adding zeros.

$4 x (x - 2) < 2 (2 x - 1) (x - 3)$

Apply the distributive property.

$4 x \cdot x + 4 x \cdot - 2 < 2 (2 x - 1) (x - 3)$

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

Move $x$ .

$4 (x \cdot x) + 4 x \cdot - 2 < 2 (2 x - 1) (x - 3)$

Multiply $x$ by $x$ .

$4 x^{2} + 4 x \cdot - 2 < 2 (2 x - 1) (x - 3)$

Multiply $- 2$ by $4$ .

$4 x^{2} - 8 x < 2 (2 x - 1) (x - 3)$

Simplify $2 (2 x - 1) (x - 3)$ .

Simplify by multiplying through.

Apply the distributive property.

$4 x^{2} - 8 x < (2 (2 x) + 2 \cdot - 1) (x - 3)$

Multiply.

Multiply $2$ by $2$ .

$4 x^{2} - 8 x < (4 x + 2 \cdot - 1) (x - 3)$

Multiply $2$ by $- 1$ .

$4 x^{2} - 8 x < (4 x - 2) (x - 3)$

Expand $(4 x - 2) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} - 8 x < 4 x (x - 3) - 2 (x - 3)$

Apply the distributive property.

$4 x^{2} - 8 x < 4 x \cdot x + 4 x \cdot - 3 - 2 (x - 3)$

Apply the distributive property.

$4 x^{2} - 8 x < 4 x \cdot x + 4 x \cdot - 3 - 2 x - 2 \cdot - 3$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$4 x^{2} - 8 x < 4 (x \cdot x) + 4 x \cdot - 3 - 2 x - 2 \cdot - 3$

Multiply $x$ by $x$ .

$4 x^{2} - 8 x < 4 x^{2} + 4 x \cdot - 3 - 2 x - 2 \cdot - 3$

Multiply $- 3$ by $4$ .

$4 x^{2} - 8 x < 4 x^{2} - 12 x - 2 x - 2 \cdot - 3$

Multiply $- 2$ by $- 3$ .

$4 x^{2} - 8 x < 4 x^{2} - 12 x - 2 x + 6$

Subtract $2 x$ from $- 12 x$ .

$4 x^{2} - 8 x < 4 x^{2} - 14 x + 6$

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

Subtract $4 x^{2}$ from both sides of the inequality.

$4 x^{2} - 8 x - 4 x^{2} < - 14 x + 6$

Add $14 x$ to both sides of the inequality.

$4 x^{2} - 8 x - 4 x^{2} + 14 x < 6$

Combine the opposite terms in $4 x^{2} - 8 x - 4 x^{2} + 14 x$ .

Subtract $4 x^{2}$ from $4 x^{2}$ .

$- 8 x + 0 + 14 x < 6$

Add $- 8 x$ and $0$ .

$- 8 x + 14 x < 6$

Add $- 8 x$ and $14 x$ .

$6 x < 6$

Divide each term in $6 x < 6$ by $6$ and simplify.

Divide each term in $6 x < 6$ by $6$ .

$\frac{6 x}{6} < \frac{6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} < \frac{6}{6}$

Divide $x$ by $1$ .

$x < \frac{6}{6}$

Simplify the right side.

Divide $6$ by $6$ .

$x < 1$

Use the inequality $x < 1$ to build the set notation.

${x | x < 1}$

Convert to Set Notation 4x(x-2)<2(2x-1)(x-3)

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