Solve 1-x/3+2leqx+1/2

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

Solve for x

$$x\geq \frac{11}{5}$$

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.

$$2\left(1-x\right)+12\leq 3\left(x+1\right)$$

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

$$2-2x+12\leq 3\left(x+1\right)$$

Add 2 and 12 to get 14.

$$14-2x\leq 3\left(x+1\right)$$

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

$$14-2x\leq 3x+3$$

Subtract 3x from both sides.

$$14-2x-3x\leq 3$$

Combine -2x and -3x to get -5x.

$$14-5x\leq 3$$

Subtract 14 from both sides.

$$-5x\leq 3-14$$

Subtract 14 from 3 to get -11.

$$-5x\leq -11$$

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

$$x\geq \frac{-11}{-5}$$

Fraction \frac{-11}{-5} can be simplified to \frac{11}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{11}{5}$$