Solve 2x-1/3-3x-1/2geq1

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

Solve for x

$$x\leq -1$$

Solution Steps

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

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

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

$$4x-2-3\left(3x-1\right)\geq 6$$

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

$$4x-2-9x+3\geq 6$$

Combine 4x and -9x to get -5x.

$$-5x-2+3\geq 6$$

Add -2 and 3 to get 1.

$$-5x+1\geq 6$$

Subtract 1 from both sides.

$$-5x\geq 6-1$$

Subtract 1 from 6 to get 5.

$$-5x\geq 5$$

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

$$x\leq \frac{5}{-5}$$

Divide 5 by -5 to get -1.

$$x\leq -1$$