Solve x-4/3-3x-1/2>4

$$\frac { x - 4 } { 3 } - \frac { 3 x - 1 } { 2 } > 4$$

Solve for x

$$x<-\frac{29}{7}$$

Solution Steps

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

$$2\left(x-4\right)-3\left(3x-1\right)>24$$

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

$$2x-8-3\left(3x-1\right)>24$$

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

$$2x-8-9x+3>24$$

Combine 2x and -9x to get -7x.

$$-7x-8+3>24$$

Add -8 and 3 to get -5.

$$-7x-5>24$$

Add 5 to both sides.

$$-7x>24+5$$

Add 24 and 5 to get 29.

$$-7x>29$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x<-\frac{29}{7}$$