Solve 1/3x-1geq(x-3)/2

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

Solve for x

$$x\leq 3$$

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.

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

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

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

Subtract 3x from both sides.

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

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

$$-x-6\geq -9$$

Add 6 to both sides.

$$-x\geq -9+6$$

Add -9 and 6 to get -3.

$$-x\geq -3$$

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

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

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$x\leq 3$$