Solve (2x+1)(3x+2)>(2x+5)(3x-1)

$$( 2 x + 1 ) ( 3 x + 2 ) > ( 2 x + 5 ) ( 3 x - 1 )$$

Solve for x

$$x<\frac{7}{6}$$

Solution Steps

Use the distributive property to multiply 2x+1 by 3x+2 and combine like terms.

$$6x^{2}+7x+2>\left(2x+5\right)\left(3x-1\right)$$

Use the distributive property to multiply 2x+5 by 3x-1 and combine like terms.

$$6x^{2}+7x+2>6x^{2}+13x-5$$

Subtract 6x^{2} from both sides.

$$6x^{2}+7x+2-6x^{2}>13x-5$$

Combine 6x^{2} and -6x^{2} to get 0.

$$7x+2>13x-5$$

Subtract 13x from both sides.

$$7x+2-13x>-5$$

Combine 7x and -13x to get -6x.

$$-6x+2>-5$$

Subtract 2 from both sides.

$$-6x>-5-2$$

Subtract 2 from -5 to get -7.

$$-6x>-7$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x<\frac{-7}{-6}$$

Fraction \frac{-7}{-6} can be simplified to \frac{7}{6} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{7}{6}$$