Solve 5x-2/3-7x-3/5>x/4

$$\frac { 5 x - 2 } { 3 } - \frac { 7 x - 3 } { 5 } > \frac { x } { 4 }$$

Solve for x

$$x>4$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 3,5,4. Since 60 is positive, the inequality direction remains the same.

$$20\left(5x-2\right)-12\left(7x-3\right)>15x$$

Use the distributive property to multiply 20 by 5x-2.

$$100x-40-12\left(7x-3\right)>15x$$

Use the distributive property to multiply -12 by 7x-3.

$$100x-40-84x+36>15x$$

Combine 100x and -84x to get 16x.

$$16x-40+36>15x$$

Add -40 and 36 to get -4.

$$16x-4>15x$$

Subtract 15x from both sides.

$$16x-4-15x>0$$

Combine 16x and -15x to get x.

$$x-4>0$$

Add 4 to both sides. Anything plus zero gives itself.

$$x>4$$