Solve 2x-x-1/5geq1/4-x

$$2x- \frac{ x-1 }{ 5 } \geq \frac{ 1 }{ 4 } -x$$

Solve for x

$$x\geq \frac{1}{56}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 5,4. Since 20 is positive, the inequality direction remains the same.

$$40x-4\left(x-1\right)\geq 5-20x$$

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

$$40x-4x+4\geq 5-20x$$

Combine 40x and -4x to get 36x.

$$36x+4\geq 5-20x$$

Add 20x to both sides.

$$36x+4+20x\geq 5$$

Combine 36x and 20x to get 56x.

$$56x+4\geq 5$$

Subtract 4 from both sides.

$$56x\geq 5-4$$

Subtract 4 from 5 to get 1.

$$56x\geq 1$$

Divide both sides by 56. Since 56 is positive, the inequality direction remains the same.

$$x\geq \frac{1}{56}$$