Solve 3(-5x-2)/2>2(9x+9)/3

$$\frac { 3 ( - 5 x - 2 ) } { 2 } > \frac { 2 ( 9 x + 9 ) } { 3 }$$

Solve for x

$$x<-\frac{2}{3}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$3\times 3\left(-5x-2\right)>2\times 2\left(9x+9\right)$$

Multiply 3 and 3 to get 9.

$$9\left(-5x-2\right)>2\times 2\left(9x+9\right)$$

Use the distributive property to multiply 9 by -5x-2.

$$-45x-18>2\times 2\left(9x+9\right)$$

Multiply 2 and 2 to get 4.

$$-45x-18>4\left(9x+9\right)$$

Use the distributive property to multiply 4 by 9x+9.

$$-45x-18>36x+36$$

Subtract 36x from both sides.

$$-45x-18-36x>36$$

Combine -45x and -36x to get -81x.

$$-81x-18>36$$

Add 18 to both sides.

$$-81x>36+18$$

Add 36 and 18 to get 54.

$$-81x>54$$

Divide both sides by -81. Since -81 is negative, the inequality direction is changed.

$$x<\frac{54}{-81}$$

Reduce the fraction \frac{54}{-81} to lowest terms by extracting and canceling out 27.

$$x<-\frac{2}{3}$$