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

x < 3 or x > 9

Step-by-step 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

x > 9 or x < 3

Step-by-step 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→

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.