Solve x+3/4leq5x-2/3

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

Solve for x

$$x\geq \frac{17}{8}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$12x+9\leq 4\left(5x-2\right)$$

Use the distributive property to multiply 4 by 5x-2.

$$12x+9\leq 20x-8$$

Subtract 20x from both sides.

$$12x+9-20x\leq -8$$

Combine 12x and -20x to get -8x.

$$-8x+9\leq -8$$

Subtract 9 from both sides.

$$-8x\leq -8-9$$

Subtract 9 from -8 to get -17.

$$-8x\leq -17$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x\geq \frac{-17}{-8}$$

Fraction \frac{-17}{-8} can be simplified to \frac{17}{8} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{17}{8}$$