Solve 2-3x/3-x-1/2leq1

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

Solve for x

$$x\geq \frac{1}{9}$$

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.

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

Use the distributive property to multiply 2 by 2-3x.

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

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

$$4-6x-3x+3\leq 6$$

Combine -6x and -3x to get -9x.

$$4-9x+3\leq 6$$

Add 4 and 3 to get 7.

$$7-9x\leq 6$$

Subtract 7 from both sides.

$$-9x\leq 6-7$$

Subtract 7 from 6 to get -1.

$$-9x\leq -1$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x\geq \frac{-1}{-9}$$

Fraction \frac{-1}{-9} can be simplified to \frac{1}{9} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{1}{9}$$