Solve 2div5-2xdiv3geqx/6

$$2 \div 5-2x \div 3 \geq \frac{ x }{ 6 }$$

Solve for x

$$x\leq \frac{12}{25}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,3,6. Since 30 is positive, the inequality direction remains the same.

$$12-10\times 2x\geq 5x$$

Multiply -10 and 2 to get -20.

$$12-20x\geq 5x$$

Subtract 5x from both sides.

$$12-20x-5x\geq 0$$

Combine -20x and -5x to get -25x.

$$12-25x\geq 0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-25x\geq -12$$

Divide both sides by -25. Since -25 is negative, the inequality direction is changed.

$$x\leq \frac{-12}{-25}$$

Fraction \frac{-12}{-25} can be simplified to \frac{12}{25} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{12}{25}$$