Solve 6-4(2x-3)<3(x+1)

$$6 - 4 ( 2 x - 3 ) < 3 ( x + 1 )$$

Solve for x

$$x>\frac{15}{11}$$

Solution Steps

Use the distributive property to multiply -4 by 2x-3.

$$6-8x+12<3\left(x+1\right)$$

Add 6 and 12 to get 18.

$$18-8x<3\left(x+1\right)$$

Use the distributive property to multiply 3 by x+1.

$$18-8x<3x+3$$

Subtract 3x from both sides.

$$18-8x-3x<3$$

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

$$18-11x<3$$

Subtract 18 from both sides.

$$-11x<3-18$$

Subtract 18 from 3 to get -15.

$$-11x<-15$$

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

$$x>\frac{-15}{-11}$$

Fraction \frac{-15}{-11} can be simplified to \frac{15}{11} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{15}{11}$$