Solve x+3/4<5x-2/3+1

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

Solve for x

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

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.

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

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

$$12x+9<20x-8+12$$

Add -8 and 12 to get 4.

$$12x+9<20x+4$$

Subtract 20x from both sides.

$$12x+9-20x<4$$

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

$$-8x+9<4$$

Subtract 9 from both sides.

$$-8x<4-9$$

Subtract 9 from 4 to get -5.

$$-8x<-5$$

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

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

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

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