Solve 3(x-1)/4-1geqx+1/2-2x+1/3

$$\frac { 3 ( x - 1 ) } { 4 } - 1 \geq \frac { x + 1 } { 2 } - \frac { 2 x + 1 } { 3 }$$

Solve for x

$$x\geq \frac{23}{11}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,2,3. Since 12 is positive, the inequality direction remains the same.

$$3\times 3\left(x-1\right)-12\geq 6\left(x+1\right)-4\left(2x+1\right)$$

Multiply 3 and 3 to get 9.

$$9\left(x-1\right)-12\geq 6\left(x+1\right)-4\left(2x+1\right)$$

Use the distributive property to multiply 9 by x-1.

$$9x-9-12\geq 6\left(x+1\right)-4\left(2x+1\right)$$

Subtract 12 from -9 to get -21.

$$9x-21\geq 6\left(x+1\right)-4\left(2x+1\right)$$

Use the distributive property to multiply 6 by x+1.

$$9x-21\geq 6x+6-4\left(2x+1\right)$$

Use the distributive property to multiply -4 by 2x+1.

$$9x-21\geq 6x+6-8x-4$$

Combine 6x and -8x to get -2x.

$$9x-21\geq -2x+6-4$$

Subtract 4 from 6 to get 2.

$$9x-21\geq -2x+2$$

Add 2x to both sides.

$$9x-21+2x\geq 2$$

Combine 9x and 2x to get 11x.

$$11x-21\geq 2$$

Add 21 to both sides.

$$11x\geq 2+21$$

Add 2 and 21 to get 23.

$$11x\geq 23$$

Divide both sides by 11. Since 11 is positive, the inequality direction remains the same.

$$x\geq \frac{23}{11}$$