Convert to Set Notation 4x(x-5)<2(2x-1)(x-6)

$4 x (x - 5) < 2 (2 x - 1) (x - 6)$

Step 1

Solve $x < 2$ .

Simplify $4 x (x - 5)$ .

Rewrite.

$0 + 0 + 4 x (x - 5) < 2 (2 x - 1) (x - 6)$

Simplify by adding zeros.

$4 x (x - 5) < 2 (2 x - 1) (x - 6)$

Apply the distributive property.

$4 x \cdot x + 4 x \cdot - 5 < 2 (2 x - 1) (x - 6)$

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

Move $x$ .

$4 (x \cdot x) + 4 x \cdot - 5 < 2 (2 x - 1) (x - 6)$

Multiply $x$ by $x$ .

$4 x^{2} + 4 x \cdot - 5 < 2 (2 x - 1) (x - 6)$

Multiply $- 5$ by $4$ .

$4 x^{2} - 20 x < 2 (2 x - 1) (x - 6)$

Simplify $2 (2 x - 1) (x - 6)$ .

Simplify by multiplying through.

Apply the distributive property.

$4 x^{2} - 20 x < (2 (2 x) + 2 \cdot - 1) (x - 6)$

Multiply.

Multiply $2$ by $2$ .

$4 x^{2} - 20 x < (4 x + 2 \cdot - 1) (x - 6)$

Multiply $2$ by $- 1$ .

$4 x^{2} - 20 x < (4 x - 2) (x - 6)$

Expand $(4 x - 2) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} - 20 x < 4 x (x - 6) - 2 (x - 6)$

Apply the distributive property.

$4 x^{2} - 20 x < 4 x \cdot x + 4 x \cdot - 6 - 2 (x - 6)$

Apply the distributive property.

$4 x^{2} - 20 x < 4 x \cdot x + 4 x \cdot - 6 - 2 x - 2 \cdot - 6$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$4 x^{2} - 20 x < 4 (x \cdot x) + 4 x \cdot - 6 - 2 x - 2 \cdot - 6$

Multiply $x$ by $x$ .

$4 x^{2} - 20 x < 4 x^{2} + 4 x \cdot - 6 - 2 x - 2 \cdot - 6$

Multiply $- 6$ by $4$ .

$4 x^{2} - 20 x < 4 x^{2} - 24 x - 2 x - 2 \cdot - 6$

Multiply $- 2$ by $- 6$ .

$4 x^{2} - 20 x < 4 x^{2} - 24 x - 2 x + 12$

Subtract $2 x$ from $- 24 x$ .

$4 x^{2} - 20 x < 4 x^{2} - 26 x + 12$

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

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

$4 x^{2} - 20 x - 4 x^{2} < - 26 x + 12$

Add $26 x$ to both sides of the inequality.

$4 x^{2} - 20 x - 4 x^{2} + 26 x < 12$

Combine the opposite terms in $4 x^{2} - 20 x - 4 x^{2} + 26 x$ .

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

$- 20 x + 0 + 26 x < 12$

Add $- 20 x$ and $0$ .

$- 20 x + 26 x < 12$

Add $- 20 x$ and $26 x$ .

$6 x < 12$

Divide each term in $6 x < 12$ by $6$ and simplify.

Divide each term in $6 x < 12$ by $6$ .

$\frac{6 x}{6} < \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} < \frac{12}{6}$

Divide $x$ by $1$ .

$x < \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$x < 2$

Step 2

Use the inequality $x < 2$ to build the set notation.

${x | x < 2}$

Step 3

Convert to Set Notation 4x(x-5)<2(2x-1)(x-6)

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