Solve 2-3(x-5)>5(1-x)

$$2 - 3 ( x - 5 ) > 5 ( 1 - x )$$

Solve for x

$$x>-6$$

Solution Steps

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

$$2-3x+15>5\left(1-x\right)$$

Add 2 and 15 to get 17.

$$17-3x>5\left(1-x\right)$$

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

$$17-3x>5-5x$$

Add 5x to both sides.

$$17-3x+5x>5$$

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

$$17+2x>5$$

Subtract 17 from both sides.

$$2x>5-17$$

Subtract 17 from 5 to get -12.

$$2x>-12$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x>\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$x>-6$$