Solve 7(x+2)-2>12(x-1)-1

$$7 ( x + 2 ) - 2 > 12 ( x - 1 ) - 1$$

Solve for x

$$x<5$$

Solution Steps

Use the distributive property to multiply 7 by x+2.

$$7x+14-2>12\left(x-1\right)-1$$

Subtract 2 from 14 to get 12.

$$7x+12>12\left(x-1\right)-1$$

Use the distributive property to multiply 12 by x-1.

$$7x+12>12x-12-1$$

Subtract 1 from -12 to get -13.

$$7x+12>12x-13$$

Subtract 12x from both sides.

$$7x+12-12x>-13$$

Combine 7x and -12x to get -5x.

$$-5x+12>-13$$

Subtract 12 from both sides.

$$-5x>-13-12$$

Subtract 12 from -13 to get -25.

$$-5x>-25$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x<\frac{-25}{-5}$$

Divide -25 by -5 to get 5.

$$x<5$$