Solve x+3/4>x/2+4x/5

$$\frac { x + 3 } { 4 } > \frac { x } { 2 } + \frac { 4 x } { 5 }$$

Solve for x

$$x<\frac{5}{7}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,2,5. Since 20 is positive, the inequality direction remains the same.

$$5\left(x+3\right)>10x+4\times 4x$$

Use the distributive property to multiply 5 by x+3.

$$5x+15>10x+4\times 4x$$

Multiply 4 and 4 to get 16.

$$5x+15>10x+16x$$

Combine 10x and 16x to get 26x.

$$5x+15>26x$$

Subtract 26x from both sides.

$$5x+15-26x>0$$

Combine 5x and -26x to get -21x.

$$-21x+15>0$$

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$-21x>-15$$

Divide both sides by -21. Since -21 is negative, the inequality direction is changed.

$$x<\frac{-15}{-21}$$

Reduce the fraction \frac{-15}{-21} to lowest terms by extracting and canceling out -3.

$$x<\frac{5}{7}$$