Solve 2x-1/3leqx-1-x/2

$$\frac{ 2x-1 }{ 3 } \leq x- \frac{ 1-x }{ 2 }$$

Solve for x

$$x\geq \frac{1}{5}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x-1\right)\leq 6x-3\left(1-x\right)$$

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

$$4x-2\leq 6x-3\left(1-x\right)$$

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

$$4x-2\leq 6x-3+3x$$

Combine 6x and 3x to get 9x.

$$4x-2\leq 9x-3$$

Subtract 9x from both sides.

$$4x-2-9x\leq -3$$

Combine 4x and -9x to get -5x.

$$-5x-2\leq -3$$

Add 2 to both sides.

$$-5x\leq -3+2$$

Add -3 and 2 to get -1.

$$-5x\leq -1$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

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

Fraction \frac{-1}{-5} can be simplified to \frac{1}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{1}{5}$$