Solve 3x+8/3>5x-1/2

$$\frac { 3 x + 8 } { 3 } > \frac { 5 x - 1 } { 2 }$$

Solve for x

$$x<\frac{19}{9}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(3x+8\right)>3\left(5x-1\right)$$

Use the distributive property to multiply 2 by 3x+8.

$$6x+16>3\left(5x-1\right)$$

Use the distributive property to multiply 3 by 5x-1.

$$6x+16>15x-3$$

Subtract 15x from both sides.

$$6x+16-15x>-3$$

Combine 6x and -15x to get -9x.

$$-9x+16>-3$$

Subtract 16 from both sides.

$$-9x>-3-16$$

Subtract 16 from -3 to get -19.

$$-9x>-19$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x<\frac{-19}{-9}$$

Fraction \frac{-19}{-9} can be simplified to \frac{19}{9} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{19}{9}$$