Solve 2x-1/3-9x+2/6leq-1

$$\frac{ 2x-1 }{ 3 } - \frac{ 9x+2 }{ 6 } \leq -1$$

Solve for x

$$x\geq \frac{2}{5}$$

Solution Steps

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

$$2\left(2x-1\right)-\left(9x+2\right)\leq -6$$

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

$$4x-2-\left(9x+2\right)\leq -6$$

To find the opposite of 9x+2, find the opposite of each term.

$$4x-2-9x-2\leq -6$$

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

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

Subtract 2 from -2 to get -4.

$$-5x-4\leq -6$$

Add 4 to both sides.

$$-5x\leq -6+4$$

Add -6 and 4 to get -2.

$$-5x\leq -2$$

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

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

Fraction \frac{-2}{-5} can be simplified to \frac{2}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{2}{5}$$