Solve -3(x+4)>7x-4(x-4)+6

$$- 3 ( x + 4 ) > 7 x - 4 ( x - 4 ) + 6$$

Solve for x

$$x<-\frac{17}{3}$$

Solution Steps

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

$$-3x-12>7x-4\left(x-4\right)+6$$

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

$$-3x-12>7x-4x+16+6$$

Combine 7x and -4x to get 3x.

$$-3x-12>3x+16+6$$

Add 16 and 6 to get 22.

$$-3x-12>3x+22$$

Subtract 3x from both sides.

$$-3x-12-3x>22$$

Combine -3x and -3x to get -6x.

$$-6x-12>22$$

Add 12 to both sides.

$$-6x>22+12$$

Add 22 and 12 to get 34.

$$-6x>34$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x<\frac{34}{-6}$$

Reduce the fraction \frac{34}{-6} to lowest terms by extracting and canceling out 2.

$$x<-\frac{17}{3}$$