Solve x+3/4leq5x-2/3+1

$$x + \frac { 3 } { 4 } \leq \frac { 5 x - 2 } { 3 } + 1$$

Solve for x

$$x\geq \frac{5}{8}$$

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.

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

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

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

Add -8 and 12 to get 4.

$$12x+9\leq 20x+4$$

Subtract 20x from both sides.

$$12x+9-20x\leq 4$$

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

$$-8x+9\leq 4$$

Subtract 9 from both sides.

$$-8x\leq 4-9$$

Subtract 9 from 4 to get -5.

$$-8x\leq -5$$

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

$$x\geq \frac{-5}{-8}$$

Fraction \frac{-5}{-8} can be simplified to \frac{5}{8} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{5}{8}$$