Solve 4/5-1+2x/2<7x-3/10

$$\frac { 4 } { 5 } - \frac { 1 + 2 x } { 2 } < \frac { 7 x - 3 } { 10 }$$

Solve for x

$$x>\frac{6}{17}$$

Solution Steps

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

$$8-5\left(1+2x\right)<7x-3$$

Use the distributive property to multiply -5 by 1+2x.

$$8-5-10x<7x-3$$

Subtract 5 from 8 to get 3.

$$3-10x<7x-3$$

Subtract 7x from both sides.

$$3-10x-7x<-3$$

Combine -10x and -7x to get -17x.

$$3-17x<-3$$

Subtract 3 from both sides.

$$-17x<-3-3$$

Subtract 3 from -3 to get -6.

$$-17x<-6$$

Divide both sides by -17. Since -17 is negative, the inequality direction is changed.

$$x>\frac{-6}{-17}$$

Fraction \frac{-6}{-17} can be simplified to \frac{6}{17} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{6}{17}$$