Solve x+2/3+4-3x/2>0

$$\frac { x + 2 } { 3 } + \frac { 4 - 3 x } { 2 } > 0$$

Solve for x

$$x<\frac{16}{7}$$

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.

$$2\left(x+2\right)+3\left(4-3x\right)>0$$

Use the distributive property to multiply 2 by x+2.

$$2x+4+3\left(4-3x\right)>0$$

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

$$2x+4+12-9x>0$$

Add 4 and 12 to get 16.

$$2x+16-9x>0$$

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

$$-7x+16>0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$-7x>-16$$

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

$$x<\frac{-16}{-7}$$

Fraction \frac{-16}{-7} can be simplified to \frac{16}{7} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{16}{7}$$