Solve x+3/2+3x-4>3x+7/3+5x-12

$$\frac { x + 3 } { 2 } + 3 x - 4 > \frac { 3 x + 7 } { 3 } + 5 x - 12$$

Solve for x

$$x<\frac{43}{15}$$

Solution Steps

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

$$3\left(x+3\right)+18x-24>2\left(3x+7\right)+30x-72$$

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

$$3x+9+18x-24>2\left(3x+7\right)+30x-72$$

Combine 3x and 18x to get 21x.

$$21x+9-24>2\left(3x+7\right)+30x-72$$

Subtract 24 from 9 to get -15.

$$21x-15>2\left(3x+7\right)+30x-72$$

Use the distributive property to multiply 2 by 3x+7.

$$21x-15>6x+14+30x-72$$

Combine 6x and 30x to get 36x.

$$21x-15>36x+14-72$$

Subtract 72 from 14 to get -58.

$$21x-15>36x-58$$

Subtract 36x from both sides.

$$21x-15-36x>-58$$

Combine 21x and -36x to get -15x.

$$-15x-15>-58$$

Add 15 to both sides.

$$-15x>-58+15$$

Add -58 and 15 to get -43.

$$-15x>-43$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x<\frac{-43}{-15}$$

Fraction \frac{-43}{-15} can be simplified to \frac{43}{15} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{43}{15}$$