Solve 3-x/4<2x-6/7

$$\frac { 3 - x } { 4 } < \frac { 2 x - 6 } { 7 }$$

Solve for x

$$x>3$$

Solution Steps

Multiply both sides of the equation by 28, the least common multiple of 4,7. Since 28 is positive, the inequality direction remains the same.

$$7\left(3-x\right)<4\left(2x-6\right)$$

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

$$21-7x<4\left(2x-6\right)$$

Use the distributive property to multiply 4 by 2x-6.

$$21-7x<8x-24$$

Subtract 8x from both sides.

$$21-7x-8x<-24$$

Combine -7x and -8x to get -15x.

$$21-15x<-24$$

Subtract 21 from both sides.

$$-15x<-24-21$$

Subtract 21 from -24 to get -45.

$$-15x<-45$$

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

$$x>\frac{-45}{-15}$$

Divide -45 by -15 to get 3.

$$x>3$$