How do I do this question:

-6|7-x|< -30

So far I have that x=2, but I know that it's more than just 2. How do I denote/find that?

first of all isolate the absolute value expression by dividing by -6, remembering that we have to reverse the inequality sign if we divide or multiply by a negative.
|7-x| > 5

then 7-x > 5 OR -7 + x > 5
-x > -2 OR x > 12
x < 2 OR x > 12

To solve the inequality -6|7-x| < -30, you have correctly started by isolating the absolute value expression by dividing both sides by -6. However, there is a mistake in the remainder of your solution.

Let's go over the correct steps to solve the inequality:

1. Divide both sides of the inequality by -6, remembering to reverse the inequality sign since we are dividing by a negative number. This gives us:

|7-x| > 5

2. Now we have an absolute value inequality. To solve it, we need to consider two cases: the expression inside the absolute value is positive, or the expression is negative.

Case 1: 7 - x is positive:
In this case, we can directly write the inequality:

7 - x > 5

Simplifying this inequality gives us:

-x > -2

Multiply both sides by -1, remembering to reverse the inequality sign:

x < 2

So for case 1, the solution is x < 2.

Case 2: 7 - x is negative:
In this case, we need to change the inequality when removing the absolute value. To do this, we multiply both sides of the inequality by -1 and reverse the inequality sign:

-(7 - x) > 5

Simplifying this inequality gives us:

-x + 7 > 5

Subtract 7 from both sides:

-x > -2

Again, multiply both sides by -1 and reverse the inequality sign:

x < 2

For case 2, the solution is also x < 2.

Combining the solutions from both cases, we find that x must be less than 2:

x < 2

Therefore, the complete solution to the inequality -6|7-x| < -30 is x < 2.