Solve x-1/2-2x-1/3>1

$$\frac { x - 1 } { 2 } - \frac { 2 x - 1 } { 3 } > 1$$

Solve for x

$$x<-7$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

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

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

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

Use the distributive property to multiply -2 by 2x-1.

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

Combine 3x and -4x to get -x.

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

Add -3 and 2 to get -1.

$$-x-1>6$$

Add 1 to both sides.

$$-x>6+1$$

Add 6 and 1 to get 7.

$$-x>7$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<-7$$