Solve x-11/5-6x/4>7

$$\frac { x - 11 } { 5 } - \frac { 6 x } { 4 } > 7$$

Solve for x

$$x<-\frac{92}{13}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 5,4. Since 20 is positive, the inequality direction remains the same.

$$4\left(x-11\right)-5\times 6x>140$$

Use the distributive property to multiply 4 by x-11.

$$4x-44-5\times 6x>140$$

Multiply -5 and 6 to get -30.

$$4x-44-30x>140$$

Combine 4x and -30x to get -26x.

$$-26x-44>140$$

Add 44 to both sides.

$$-26x>140+44$$

Add 140 and 44 to get 184.

$$-26x>184$$

Divide both sides by -26. Since -26 is negative, the inequality direction is changed.

$$x<\frac{184}{-26}$$

Reduce the fraction \frac{184}{-26} to lowest terms by extracting and canceling out 2.

$$x<-\frac{92}{13}$$