Question

1. -1 -6x -6 > -11 -7x

Explanation:

Step1: Simplify left - hand side

Combine like terms: $-1-6x - 6=-6x-(1 + 6)=-6x-7$.
The inequality becomes $-6x-7>-11 - 7x$.

Step2: Add \(7x\) to both sides

Using the addition property of inequalities: $-6x + 7x-7>-11-7x + 7x$.
Simplify to get $x-7>-11$.

Step3: Add \(7\) to both sides

Using the addition property of inequalities: $x-7 + 7>-11 + 7$.
Simplify to get $x>-4$.

Answer:

The solution of the inequality is \(x>-4\). On the number - line, we represent it by an open circle at \(-4\) (since \(x=-4\) is not included) and a ray extending to the right.