Solve x-1/6leq5x-1/3

$$\frac { x - 1 } { 6 } \leq \frac { 5 x - 1 } { 3 }$$

Solve for x

$$x\geq \frac{1}{9}$$

Solution Steps

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

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

Use the distributive property to multiply 2 by 5x-1.

$$x-1\leq 10x-2$$

Subtract 10x from both sides.

$$x-1-10x\leq -2$$

Combine x and -10x to get -9x.

$$-9x-1\leq -2$$

Add 1 to both sides.

$$-9x\leq -2+1$$

Add -2 and 1 to get -1.

$$-9x\leq -1$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x\geq \frac{-1}{-9}$$

Fraction \frac{-1}{-9} can be simplified to \frac{1}{9} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{1}{9}$$