Solve 2x-1/2-5x+2/6-xleq-1

$$\frac { 2 x - 1 } { 2 } - \frac { 5 x + 2 } { 6 } - x \leq - 1$$

Solve for x

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

Solution Steps

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

$$3\left(2x-1\right)-\left(5x+2\right)-6x\leq -6$$

Use the distributive property to multiply 3 by 2x-1.

$$6x-3-\left(5x+2\right)-6x\leq -6$$

To find the opposite of 5x+2, find the opposite of each term.

$$6x-3-5x-2-6x\leq -6$$

Combine 6x and -5x to get x.

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

Subtract 2 from -3 to get -5.

$$x-5-6x\leq -6$$

Combine x and -6x to get -5x.

$$-5x-5\leq -6$$

Add 5 to both sides.

$$-5x\leq -6+5$$

Add -6 and 5 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.

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