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

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

Solve for x

$$x<\frac{6}{11}$$

Solution Steps

Use the distributive property to multiply 3 by 2-x.

$$6-3x>2\left(3x+x\right)$$

Combine 3x and x to get 4x.

$$6-3x>2\times 4x$$

Multiply 2 and 4 to get 8.

$$6-3x>8x$$

Subtract 8x from both sides.

$$6-3x-8x>0$$

Combine -3x and -8x to get -11x.

$$6-11x>0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-11x>-6$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x<\frac{-6}{-11}$$

Fraction \frac{-6}{-11} can be simplified to \frac{6}{11} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{6}{11}$$