Solve 6/5-x+7/6>-(2-x+4/2)

$$\frac { 6 } { 5 } - \frac { x + 7 } { 6 } > - ( 2 - \frac { x + 4 } { 2 } )$$

Solve for x

$$x<\frac{1}{20}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,6. Since 30 is positive, the inequality direction remains the same.

$$36-5\left(x+7\right)>-30\left(2-\frac{x+4}{2}\right)$$

Use the distributive property to multiply -5 by x+7.

$$36-5x-35>-30\left(2-\frac{x+4}{2}\right)$$

Subtract 35 from 36 to get 1.

$$1-5x>-30\left(2-\frac{x+4}{2}\right)$$

Use the distributive property to multiply -30 by 2-\frac{x+4}{2}.

$$1-5x>-60-30\left(-\frac{x+4}{2}\right)$$

Multiply -30 and -1 to get 30.

$$1-5x>-60+30\times \frac{x+4}{2}$$

Cancel out 2, the greatest common factor in 30 and 2.

$$1-5x>-60+15\left(x+4\right)$$

Use the distributive property to multiply 15 by x+4.

$$1-5x>-60+15x+60$$

Add -60 and 60 to get 0.

$$1-5x>15x$$

Subtract 15x from both sides.

$$1-5x-15x>0$$

Combine -5x and -15x to get -20x.

$$1-20x>0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-20x>-1$$

Divide both sides by -20. Since -20 is negative, the inequality direction is changed.

$$x<\frac{-1}{-20}$$

Fraction \frac{-1}{-20} can be simplified to \frac{1}{20} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{1}{20}$$