$$\frac{ x }{ 10 } + \frac{ x }{ -11 } -6 > \frac{ x }{ 7 }$$
Solve for x
$x<-\frac{4620}{103}$
Solution Steps
Multiply both sides of the equation by $770$, the least common multiple of $10,-11,7$. Since $770$ is positive, the inequality direction remains the same.
$$77x-70x-4620>110x$$
Combine $77x$ and $-70x$ to get $7x$.
$$7x-4620>110x$$
Subtract $110x$ from both sides.
$$7x-4620-110x>0$$
Combine $7x$ and $-110x$ to get $-103x$.
$$-103x-4620>0$$
Add $4620$ to both sides. Anything plus zero gives itself.
$$-103x>4620$$
Divide both sides by $-103$. Since $-103$ is negative, the inequality direction is changed.
