Solve (2x+2+3x-1/5<10x+1/2)

$$( 2 x + 2 + \frac { 3 x - 1 } { 5 } < \frac { 10 x + 1 } { 2 } )$$

Solve for x

$$x>\frac{13}{24}$$

Solution Steps

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

$$20x+20+2\left(3x-1\right)<5\left(10x+1\right)$$

Use the distributive property to multiply 2 by 3x-1.

$$20x+20+6x-2<5\left(10x+1\right)$$

Combine 20x and 6x to get 26x.

$$26x+20-2<5\left(10x+1\right)$$

Subtract 2 from 20 to get 18.

$$26x+18<5\left(10x+1\right)$$

Use the distributive property to multiply 5 by 10x+1.

$$26x+18<50x+5$$

Subtract 50x from both sides.

$$26x+18-50x<5$$

Combine 26x and -50x to get -24x.

$$-24x+18<5$$

Subtract 18 from both sides.

$$-24x<5-18$$

Subtract 18 from 5 to get -13.

$$-24x<-13$$

Divide both sides by -24. Since -24 is negative, the inequality direction is changed.

$$x>\frac{-13}{-24}$$

Fraction \frac{-13}{-24} can be simplified to \frac{13}{24} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{13}{24}$$