Question

to

Answer 1

first add 3 to both sides

then use the theorem
\[\large |a|>b\qquad\Leftrightarrow\qquad a>b\vee a<-b \]

Answer 2

2x + 7 >13

Answer 3

@helder_edwin

Answer 4

That's half of the answer.
2x + 7 > 13 means 2x > 13 - 7 2x > 6 so x > 3
But then you have to do the other half.
-(2x+7) > 13 means 2x + 7 < -13 (The inequality sign flipped because we multiplied by a negative number. If you want me to explain this half of the question more, let me know.
2x + 7 < -13 means 2x < -13 - 7 2x < -20 so x < -10.
The answer is a combination of these two.
ANSWER: x > 3 OR x<-10

Answer 5

These are tricky. helder_edwin is correct that you have to know the theorem (or rule).
There are two types of questions.
Easier example of a 'LESS THAN' type:

If they say |x-1|<5 then re-write it as:
-5 < x-1 < 5 now add 1 to each part to get 'x' alone.
-4 < x < 6 So c is between -4 and 6.

For your type of question, it's a different rule.

Easier example of your type of question (a 'GREATER THAN' type): |x-2|>7
Remove the absolute value signs and re-write it as (x-2) > 7 OR -(x-2) > 7
Then remember the rule: If you multiply (or divide) an inequality by a negative number, you must switch the direction of the inequality sign!
So (x-2)>7 becomes x >9 and the right hand side
of the "OR" becomes (x-2)<-7 and then simplifies to x < -5.
So answer is: x>9 OR x<-5. The OR sign is like a capital U or V sometimes. In logic, they use a V. In statistics, they use U to mean OR.