Solve 2x-1/3-3x-5/6leqx+2/3

$$\frac { 2 x - 1 } { 3 } - \frac { 3 x - 5 } { 6 } \leq \frac { x + 2 } { 3 }$$

Solve for x

$$x\geq -1$$

Solution Steps

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

$$2\left(2x-1\right)-\left(3x-5\right)\leq 2\left(x+2\right)$$

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

$$4x-2-\left(3x-5\right)\leq 2\left(x+2\right)$$

To find the opposite of 3x-5, find the opposite of each term.

$$4x-2-3x-\left(-5\right)\leq 2\left(x+2\right)$$

The opposite of -5 is 5.

$$4x-2-3x+5\leq 2\left(x+2\right)$$

Combine 4x and -3x to get x.

$$x-2+5\leq 2\left(x+2\right)$$

Add -2 and 5 to get 3.

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

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

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

Subtract 2x from both sides.

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

Combine x and -2x to get -x.

$$-x+3\leq 4$$

Subtract 3 from both sides.

$$-x\leq 4-3$$

Subtract 3 from 4 to get 1.

$$-x\leq 1$$

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

$$x\geq -1$$