Solve the Inequality for x 2x(2x-1)-5x<4x^2-x

$2 x (2 x - 1) - 5 x < 4 x^{2} - x$

Simplify $2 x (2 x - 1) - 5 x$ .

Simplify each term.

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $2$ .

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

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Subtract $5 x$ from $- 2 x$ .

$4 x^{2} - 7 x < 4 x^{2} - x$

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

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

$4 x^{2} - 7 x - 4 x^{2} < - x$

Add $x$ to both sides of the inequality.

$4 x^{2} - 7 x - 4 x^{2} + x < 0$

Combine the opposite terms in $4 x^{2} - 7 x - 4 x^{2} + x$ .

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

$- 7 x + 0 + x < 0$

Add $- 7 x$ and $0$ .

$- 7 x + x < 0$

Add $- 7 x$ and $x$ .

$- 6 x < 0$

Divide each term in $- 6 x < 0$ by $- 6$ and simplify.

Divide each term in $- 6 x < 0$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} > \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} > \frac{0}{- 6}$

Divide $x$ by $1$ .

$x > \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$x > 0$

The result can be shown in multiple forms.

Inequality Form:

$x > 0$

Interval Notation:

$(0, \infty)$

Solve the Inequality for x 2x(2x-1)-5x<4x^2-x

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