Solve 2x+1/3-x-1/6geq2

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

Solve for x

$$x\geq 3$$

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.

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

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

$$4x+2-\left(x-1\right)\geq 12$$

To find the opposite of x-1, find the opposite of each term.

$$4x+2-x-\left(-1\right)\geq 12$$

The opposite of -1 is 1.

$$4x+2-x+1\geq 12$$

Combine 4x and -x to get 3x.

$$3x+2+1\geq 12$$

Add 2 and 1 to get 3.

$$3x+3\geq 12$$

Subtract 3 from both sides.

$$3x\geq 12-3$$

Subtract 3 from 12 to get 9.

$$3x\geq 9$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x\geq \frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x\geq 3$$