Solve x-1/4-x-1/3geq2+1-2x/6

$$\frac { x - 1 } { 4 } - \frac { x - 1 } { 3 } \geq 2 + \frac { 1 - 2 x } { 6 }$$

Solve for x

$$x\geq \frac{25}{3}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3,6. Since 12 is positive, the inequality direction remains the same.

$$3\left(x-1\right)-4\left(x-1\right)\geq 24+2\left(1-2x\right)$$

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

$$3x-3-4\left(x-1\right)\geq 24+2\left(1-2x\right)$$

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

$$3x-3-4x+4\geq 24+2\left(1-2x\right)$$

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

$$-x-3+4\geq 24+2\left(1-2x\right)$$

Add -3 and 4 to get 1.

$$-x+1\geq 24+2\left(1-2x\right)$$

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

$$-x+1\geq 24+2-4x$$

Add 24 and 2 to get 26.

$$-x+1\geq 26-4x$$

Add 4x to both sides.

$$-x+1+4x\geq 26$$

Combine -x and 4x to get 3x.

$$3x+1\geq 26$$

Subtract 1 from both sides.

$$3x\geq 26-1$$

Subtract 1 from 26 to get 25.

$$3x\geq 25$$

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

$$x\geq \frac{25}{3}$$