Solve x+1/3-2x-3/2leq1/6

$$\frac { x + 1 } { 3 } - \frac { 2 x - 3 } { 2 } \leq \frac { 1 } { 6 }$$

Solve for x

$$x\geq \frac{5}{2}$$

Solution Steps

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

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

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

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

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

$$2x+2-6x+9\leq 1$$

Combine 2x and -6x to get -4x.

$$-4x+2+9\leq 1$$

Add 2 and 9 to get 11.

$$-4x+11\leq 1$$

Subtract 11 from both sides.

$$-4x\leq 1-11$$

Subtract 11 from 1 to get -10.

$$-4x\leq -10$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\geq \frac{-10}{-4}$$

Reduce the fraction \frac{-10}{-4} to lowest terms by extracting and canceling out -2.

$$x\geq \frac{5}{2}$$