Solve x-1/5-x-1/3<5

$$\frac { x - 1 } { 5 } - \frac { x - 1 } { 3 } < 5$$

Solve for x

$$x>-\frac{73}{2}$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 5,3. Since 15 is positive, the inequality direction remains the same.

$$3\left(x-1\right)-5\left(x-1\right)<75$$

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

$$3x-3-5\left(x-1\right)<75$$

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

$$3x-3-5x+5<75$$

Combine 3x and -5x to get -2x.

$$-2x-3+5<75$$

Add -3 and 5 to get 2.

$$-2x+2<75$$

Subtract 2 from both sides.

$$-2x<75-2$$

Subtract 2 from 75 to get 73.

$$-2x<73$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x>-\frac{73}{2}$$