Solve (x+5)/7>(3x-9)/2

$$\frac { ( x + 5 ) } { 7 } > \frac { ( 3 x - 9 ) } { 2 }$$

Solve for x

$$x<\frac{73}{19}$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 7,2. Since 14 is positive, the inequality direction remains the same.

$$2\left(x+5\right)>7\left(3x-9\right)$$

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

$$2x+10>7\left(3x-9\right)$$

Use the distributive property to multiply 7 by 3x-9.

$$2x+10>21x-63$$

Subtract 21x from both sides.

$$2x+10-21x>-63$$

Combine 2x and -21x to get -19x.

$$-19x+10>-63$$

Subtract 10 from both sides.

$$-19x>-63-10$$

Subtract 10 from -63 to get -73.

$$-19x>-73$$

Divide both sides by -19. Since -19 is negative, the inequality direction is changed.

$$x<\frac{-73}{-19}$$

Fraction \frac{-73}{-19} can be simplified to \frac{73}{19} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{73}{19}$$