Solve 2(3x+7)+19>3(6x-1)

$$2 ( 3 x + 7 ) + 19 > 3 ( 6 x - 1 )$$

Solve for x

$$x<3$$

Solution Steps

Use the distributive property to multiply 2 by 3x+7.

$$6x+14+19>3\left(6x-1\right)$$

Add 14 and 19 to get 33.

$$6x+33>3\left(6x-1\right)$$

Use the distributive property to multiply 3 by 6x-1.

$$6x+33>18x-3$$

Subtract 18x from both sides.

$$6x+33-18x>-3$$

Combine 6x and -18x to get -12x.

$$-12x+33>-3$$

Subtract 33 from both sides.

$$-12x>-3-33$$

Subtract 33 from -3 to get -36.

$$-12x>-36$$

Divide both sides by -12. Since -12 is negative, the inequality direction is changed.

$$x<\frac{-36}{-12}$$

Divide -36 by -12 to get 3.

$$x<3$$