Solve 10x-5x+10-5-7<3x+5+10-x

$$10 x - 5 x + 10 - 5 - 7 < 3 x + 5 + 10 - x$$

Solve for x

$$x<\frac{17}{3}$$

Solution Steps

Combine 10x and -5x to get 5x.

$$5x+10-5-7<3x+5+10-x$$

Subtract 5 from 10 to get 5.

$$5x+5-7<3x+5+10-x$$

Subtract 7 from 5 to get -2.

$$5x-2<3x+5+10-x$$

Add 5 and 10 to get 15.

$$5x-2<3x+15-x$$

Combine 3x and -x to get 2x.

$$5x-2<2x+15$$

Subtract 2x from both sides.

$$5x-2-2x<15$$

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

$$3x-2<15$$

Add 2 to both sides.

$$3x<15+2$$

Add 15 and 2 to get 17.

$$3x<17$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x<\frac{17}{3}$$