Solve 70-5x-1/2+1/5>x+1/10

$$70 - \frac { 5 x - 1 } { 2 } + \frac { 1 } { 5 } > \frac { x + 1 } { 10 }$$

Solve for x

$$x<\frac{353}{13}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5,10. Since 10 is positive, the inequality direction remains the same.

$$700-5\left(5x-1\right)+2>x+1$$

Use the distributive property to multiply -5 by 5x-1.

$$700-25x+5+2>x+1$$

Add 700 and 5 to get 705.

$$705-25x+2>x+1$$

Add 705 and 2 to get 707.

$$707-25x>x+1$$

Subtract x from both sides.

$$707-25x-x>1$$

Combine -25x and -x to get -26x.

$$707-26x>1$$

Subtract 707 from both sides.

$$-26x>1-707$$

Subtract 707 from 1 to get -706.

$$-26x>-706$$

Divide both sides by -26. Since -26 is negative, the inequality direction is changed.

$$x<\frac{-706}{-26}$$

Reduce the fraction \frac{-706}{-26} to lowest terms by extracting and canceling out -2.

$$x<\frac{353}{13}$$