Solve the Inequality for x 2x(3x-2)+6x<6x^2-5x

$2 x (3 x - 2) + 6 x < 6 x^{2} - 5 x$

Step 1

Simplify $2 x (3 x - 2) + 6 x$ .

Simplify each term.

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 2 + 6 x < 6 x^{2} - 5 x$

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot - 2 + 6 x < 6 x^{2} - 5 x$

Multiply $- 2$ by $2$ .

$2 \cdot 3 x \cdot x - 4 x + 6 x < 6 x^{2} - 5 x$

Simplify each term.

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

Move $x$ .

$2 \cdot 3 (x \cdot x) - 4 x + 6 x < 6 x^{2} - 5 x$

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} - 4 x + 6 x < 6 x^{2} - 5 x$

Multiply $2$ by $3$ .

$6 x^{2} - 4 x + 6 x < 6 x^{2} - 5 x$

Add $- 4 x$ and $6 x$ .

$6 x^{2} + 2 x < 6 x^{2} - 5 x$

Step 2

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

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

$6 x^{2} + 2 x - 6 x^{2} < - 5 x$

Add $5 x$ to both sides of the inequality.

$6 x^{2} + 2 x - 6 x^{2} + 5 x < 0$

Combine the opposite terms in $6 x^{2} + 2 x - 6 x^{2} + 5 x$ .

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

$2 x + 0 + 5 x < 0$

Add $2 x$ and $0$ .

$2 x + 5 x < 0$

Add $2 x$ and $5 x$ .

$7 x < 0$

Step 3

Divide each term in $7 x < 0$ by $7$ and simplify.

Divide each term in $7 x < 0$ by $7$ .

$\frac{7 x}{7} < \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} < \frac{0}{7}$

Divide $x$ by $1$ .

$x < \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$x < 0$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 0$

Interval Notation:

$(- \infty, 0)$

Solve the Inequality for x 2x(3x-2)+6x<6x^2-5x

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