Solve for x 6x(x-3)<2(3x-1)(x-4)

$6 x (x - 3) < 2 (3 x - 1) (x - 4)$

Step 1

Simplify $6 x (x - 3)$ .

Rewrite.

$0 + 0 + 6 x (x - 3) < 2 (3 x - 1) (x - 4)$

Simplify by adding zeros.

$6 x (x - 3) < 2 (3 x - 1) (x - 4)$

Apply the distributive property.

$6 x \cdot x + 6 x \cdot - 3 < 2 (3 x - 1) (x - 4)$

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

Move $x$ .

$6 (x \cdot x) + 6 x \cdot - 3 < 2 (3 x - 1) (x - 4)$

Multiply $x$ by $x$ .

$6 x^{2} + 6 x \cdot - 3 < 2 (3 x - 1) (x - 4)$

Multiply $- 3$ by $6$ .

$6 x^{2} - 18 x < 2 (3 x - 1) (x - 4)$

Step 2

Simplify $2 (3 x - 1) (x - 4)$ .

Simplify by multiplying through.

Apply the distributive property.

$6 x^{2} - 18 x < (2 (3 x) + 2 \cdot - 1) (x - 4)$

Multiply.

Multiply $3$ by $2$ .

$6 x^{2} - 18 x < (6 x + 2 \cdot - 1) (x - 4)$

Multiply $2$ by $- 1$ .

$6 x^{2} - 18 x < (6 x - 2) (x - 4)$

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

Apply the distributive property.

$6 x^{2} - 18 x < 6 x (x - 4) - 2 (x - 4)$

Apply the distributive property.

$6 x^{2} - 18 x < 6 x \cdot x + 6 x \cdot - 4 - 2 (x - 4)$

Apply the distributive property.

$6 x^{2} - 18 x < 6 x \cdot x + 6 x \cdot - 4 - 2 x - 2 \cdot - 4$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$6 x^{2} - 18 x < 6 (x \cdot x) + 6 x \cdot - 4 - 2 x - 2 \cdot - 4$

Multiply $x$ by $x$ .

$6 x^{2} - 18 x < 6 x^{2} + 6 x \cdot - 4 - 2 x - 2 \cdot - 4$

Multiply $- 4$ by $6$ .

$6 x^{2} - 18 x < 6 x^{2} - 24 x - 2 x - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$6 x^{2} - 18 x < 6 x^{2} - 24 x - 2 x + 8$

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

$6 x^{2} - 18 x < 6 x^{2} - 26 x + 8$

Step 3

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

Subtract $6 x^{2}$ from both sides of the inequality.

$6 x^{2} - 18 x - 6 x^{2} < - 26 x + 8$

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

$6 x^{2} - 18 x - 6 x^{2} + 26 x < 8$

Combine the opposite terms in $6 x^{2} - 18 x - 6 x^{2} + 26 x$ .

Subtract $6 x^{2}$ from $6 x^{2}$ .

$- 18 x + 0 + 26 x < 8$

Add $- 18 x$ and $0$ .

$- 18 x + 26 x < 8$

Add $- 18 x$ and $26 x$ .

$8 x < 8$

Step 4

Divide each term in $8 x < 8$ by $8$ and simplify.

Divide each term in $8 x < 8$ by $8$ .

$\frac{8 x}{8} < \frac{8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} < \frac{8}{8}$

Divide $x$ by $1$ .

$x < \frac{8}{8}$

Simplify the right side.

Divide $8$ by $8$ .

$x < 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 1$

Interval Notation:

$(- \infty, 1)$

Step 6

Solve for x 6x(x-3)<2(3x-1)(x-4)

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