Solve x/7-3>x-4/3+1

$$\frac{ x }{ 7 } -3 > \frac{ x-4 }{ 3 } +1$$

Solve for x

$$x<-14$$

Solution Steps

Multiply both sides of the equation by 21, the least common multiple of 7,3. Since 21 is positive, the inequality direction remains the same.

$$3x-63>7\left(x-4\right)+21$$

Use the distributive property to multiply 7 by x-4.

$$3x-63>7x-28+21$$

Add -28 and 21 to get -7.

$$3x-63>7x-7$$

Subtract 7x from both sides.

$$3x-63-7x>-7$$

Combine 3x and -7x to get -4x.

$$-4x-63>-7$$

Add 63 to both sides.

$$-4x>-7+63$$

Add -7 and 63 to get 56.

$$-4x>56$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{56}{-4}$$

Divide 56 by -4 to get -14.

$$x<-14$$