Solve (1/5(x-10)>x-1/10-2-x/15

$$( \frac { 1 } { 5 } ( x - 10 ) > \frac { x - 1 } { 10 } - \frac { 2 - x } { 15 }$$

Solve for x

$$x>53$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,10,15. Since 30 is positive, the inequality direction remains the same.

$$6\left(x-10\right)>3\left(x-1\right)-2\left(2-x\right)$$

Use the distributive property to multiply 6 by x-10.

$$6x-60>3\left(x-1\right)-2\left(2-x\right)$$

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

$$6x-60>3x-3-2\left(2-x\right)$$

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

$$6x-60>3x-3-4+2x$$

Subtract 4 from -3 to get -7.

$$6x-60>3x-7+2x$$

Combine 3x and 2x to get 5x.

$$6x-60>5x-7$$

Subtract 5x from both sides.

$$6x-60-5x>-7$$

Combine 6x and -5x to get x.

$$x-60>-7$$

Add 60 to both sides.

$$x>-7+60$$

Add -7 and 60 to get 53.

$$x>53$$