Question

So I copied this off from my teacher she was showing this on the board but I need help showing my work on this so that she doesn’t know I copied it which I think she wouldn’t but you never know

Answer 1

x < 3 or x > 9

Explanation:

given 6| x - 6 | + 7 > 25 ( subtract 7 from both sides )

6| x - 6 | > 18 ( divide both sides by 6 )

| x - 6 | > 3

Inequalities of the form | x | > a always have solutions of the form

x < - a OR x > a, hence

x - 6 < - 3 or x - 6 > 3 ( add 6 to both sides in both inequalities )

x < 3 or x > 9

Answer 2

Answer: x > 9 or x < 3

Explanation:

Step 1: Isolate the absolute value expression.

6 | x - 6 | + 7 > 25

6 | x - 6 | > 18 subtracted 7 from both sides

| x - 6 | > 3 divided both sides by 3

Step 2: Solve for x.

Note: the absolute value symbol makes the value positive, so the value inside could be positive or negative. We need to find both solutions.

If inside is negative

-(x - 6) > 3

x - 6 < -3 divided both sides by -1 which flipped the inequality

x < 3 added 6 to both sides

If inside is positive

+(x - 6) > 3

x - 6 > 3 distributed +1, which didn't change the inequality

x > 9 added 6 to both sides

Step 3: Graph the solution

←-------------o -3 9 o--------------→