Solve 4/5-x+7/10>-(2-x+4/2)

$$\frac{ 4 }{ 5 } - \frac{ x+7 }{ 10 } > -(2- \frac{ x+4 }{ 2 } )$$

Solve for x

$$x<\frac{1}{6}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,10. Since 10 is positive, the inequality direction remains the same.

$$8-\left(x+7\right)>-10\left(2-\frac{x+4}{2}\right)$$

To find the opposite of x+7, find the opposite of each term.

$$8-x-7>-10\left(2-\frac{x+4}{2}\right)$$

Subtract 7 from 8 to get 1.

$$1-x>-10\left(2-\frac{x+4}{2}\right)$$

Use the distributive property to multiply -10 by 2-\frac{x+4}{2}.

$$1-x>-20-10\left(-\frac{x+4}{2}\right)$$

Multiply -10 and -1 to get 10.

$$1-x>-20+10\times \frac{x+4}{2}$$

Cancel out 2, the greatest common factor in 10 and 2.

$$1-x>-20+5\left(x+4\right)$$

Use the distributive property to multiply 5 by x+4.

$$1-x>-20+5x+20$$

Add -20 and 20 to get 0.

$$1-x>5x$$

Subtract 5x from both sides.

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

Combine -x and -5x to get -6x.

$$1-6x>0$$

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

$$-6x>-1$$

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

$$x<\frac{-1}{-6}$$

Fraction \frac{-1}{-6} can be simplified to \frac{1}{6} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{1}{6}$$