Solve x+2/2>x+3/3-(1-3x)

$$\frac { x + 2 } { 2 } > \frac { x + 3 } { 3 } - ( 1 - 3 x )$$

Solve for x

$$x<\frac{6}{17}$$

Solution Steps

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

$$3\left(x+2\right)>2\left(x+3\right)-6\left(1-3x\right)$$

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

$$3x+6>2\left(x+3\right)-6\left(1-3x\right)$$

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

$$3x+6>2x+6-6\left(1-3x\right)$$

Use the distributive property to multiply -6 by 1-3x.

$$3x+6>2x+6-6+18x$$

Subtract 6 from 6 to get 0.

$$3x+6>2x+18x$$

Combine 2x and 18x to get 20x.

$$3x+6>20x$$

Subtract 20x from both sides.

$$3x+6-20x>0$$

Combine 3x and -20x to get -17x.

$$-17x+6>0$$

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

$$-17x>-6$$

Divide both sides by -17. Since -17 is negative, the inequality direction is changed.

$$x<\frac{-6}{-17}$$

Fraction \frac{-6}{-17} can be simplified to \frac{6}{17} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{6}{17}$$