Solve x-2/3-2x-4/5leq0

$$\frac { x - 2 } { 3 } - \frac { 2 x - 4 } { 5 } \leq 0$$

Solve for x

$$x\geq 2$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 3,5. Since 15 is positive, the inequality direction remains the same.

$$5\left(x-2\right)-3\left(2x-4\right)\leq 0$$

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

$$5x-10-3\left(2x-4\right)\leq 0$$

Use the distributive property to multiply -3 by 2x-4.

$$5x-10-6x+12\leq 0$$

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

$$-x-10+12\leq 0$$

Add -10 and 12 to get 2.

$$-x+2\leq 0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-x\leq -2$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq \frac{-2}{-1}$$

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x\geq 2$$