Let Z be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of Z? A) 11 B) 19 C) 101 D) 111 E) 1111

Please explain why the answer works!!

x = 18

Step-by-step explanation:

Solve for x:

15 (x - 20) - 21 = 6 - 3 (x + 1)

Hint: | Distribute 15 over x - 20.

15 (x - 20) = 15 x - 300:

15 x - 300 - 21 = 6 - 3 (x + 1)

Hint: | Group like terms in 15 x - 300 - 21.

Grouping like terms, 15 x - 300 - 21 = 15 x + (-300 - 21):

15 x + (-300 - 21) = 6 - 3 (x + 1)

Hint: | Evaluate -300 - 21.

-300 - 21 = -321:

15 x + -321 = 6 - 3 (x + 1)

Hint: | Distribute -3 over x + 1.

-3 (x + 1) = -3 x - 3:

15 x - 321 = -3 x - 3 + 6

Hint: | Group like terms in -3 x - 3 + 6.

Grouping like terms, -3 x - 3 + 6 = (6 - 3) - 3 x:

15 x - 321 = (6 - 3) - 3 x

Hint: | Evaluate 6 - 3.

6 - 3 = 3:

15 x - 321 = 3 - 3 x

Hint: | Move terms with x to the left hand side.

Add 3 x to both sides:

15 x + 3 x - 321 = (3 x - 3 x) + 3

Hint: | Look for the difference of two identical terms.

3 x - 3 x = 0:

15 x + 3 x - 321 = 3

Hint: | Group like terms in 15 x + 3 x - 321.

Grouping like terms, 15 x + 3 x - 321 = (15 x + 3 x) - 321:

(15 x + 3 x) - 321 = 3

Hint: | Add like terms in 15 x + 3 x.

15 x + 3 x = 18 x:

18 x - 321 = 3

Hint: | Isolate terms with x to the left hand side.

Add 321 to both sides:

18 x + (321 - 321) = 321 + 3

Hint: | Look for the difference of two identical terms.

321 - 321 = 0:

18 x = 3 + 321

Hint: | Evaluate 3 + 321.

3 + 321 = 324:

18 x = 324

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 18 x = 324 by 18:

(18 x)/18 = 324/18

Hint: | Any nonzero number divided by itself is one.

18/18 = 1:

x = 324/18

Hint: | Reduce 324/18 to lowest terms. Start by finding the GCD of 324 and 18.

The gcd of 324 and 18 is 18, so 324/18 = (18×18)/(18×1) = 18/18×18 = 18:

x = 18