Solve =11+x/2-2x+1/3leq1

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

Solve for x

$$x\geq -5$$

Solution Steps

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

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

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

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

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

$$3+3x-4x-2\leq 6$$

Combine 3x and -4x to get -x.

$$3-x-2\leq 6$$

Subtract 2 from 3 to get 1.

$$1-x\leq 6$$

Subtract 1 from both sides.

$$-x\leq 6-1$$

Subtract 1 from 6 to get 5.

$$-x\leq 5$$

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

$$x\geq -5$$