Solve 7-5x/2-1+1/5>x+1/10

$$7 - \frac { 5 x } { 2 } - 1 + \frac { 1 } { 5 } > \frac { x + 1 } { 10 }$$

Solve for x

$$x<\frac{61}{26}$$

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.

$$70-5\times 5x-10+2>x+1$$

Multiply -5 and 5 to get -25.

$$70-25x-10+2>x+1$$

Subtract 10 from 70 to get 60.

$$60-25x+2>x+1$$

Add 60 and 2 to get 62.

$$62-25x>x+1$$

Subtract x from both sides.

$$62-25x-x>1$$

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

$$62-26x>1$$

Subtract 62 from both sides.

$$-26x>1-62$$

Subtract 62 from 1 to get -61.

$$-26x>-61$$

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

$$x<\frac{-61}{-26}$$

Fraction \frac{-61}{-26} can be simplified to \frac{61}{26} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{61}{26}$$