Solve 4(5x-1)+2(3x+1)^2>3x(6x+5)-2x-3

$$4 ( 5 x - 1 ) + 2 ( 3 x + 1 ) ^ { 2 } > 3 x ( 6 x + 5 ) - 2 x - 3$$

Solve for x

$$x>-\frac{1}{19}$$

Solution Steps

Use the distributive property to multiply 4 by 5x-1.

$$20x-4+2\left(3x+1\right)^{2}>3x\left(6x+5\right)-2x-3$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+1\right)^{2}.

$$20x-4+2\left(9x^{2}+6x+1\right)>3x\left(6x+5\right)-2x-3$$

Use the distributive property to multiply 2 by 9x^{2}+6x+1.

$$20x-4+18x^{2}+12x+2>3x\left(6x+5\right)-2x-3$$

Combine 20x and 12x to get 32x.

$$32x-4+18x^{2}+2>3x\left(6x+5\right)-2x-3$$

Add -4 and 2 to get -2.

$$32x-2+18x^{2}>3x\left(6x+5\right)-2x-3$$

Use the distributive property to multiply 3x by 6x+5.

$$32x-2+18x^{2}>18x^{2}+15x-2x-3$$

Combine 15x and -2x to get 13x.

$$32x-2+18x^{2}>18x^{2}+13x-3$$

Subtract 18x^{2} from both sides.

$$32x-2+18x^{2}-18x^{2}>13x-3$$

Combine 18x^{2} and -18x^{2} to get 0.

$$32x-2>13x-3$$

Subtract 13x from both sides.

$$32x-2-13x>-3$$

Combine 32x and -13x to get 19x.

$$19x-2>-3$$

Add 2 to both sides.

$$19x>-3+2$$

Add -3 and 2 to get -1.

$$19x>-1$$

Divide both sides by 19. Since 19 is positive, the inequality direction remains the same.

$$x>-\frac{1}{19}$$