Question

How many solutions are there to the equation below 9x + 27 = 9( x + 2 ) + 9

Answer 1

9x + 27 = 9(x + 2) + 9

Simplify both sides of equation:

9x + 27 = 9(x + 2) + 9

9x + 27 = (9)(x) + (9)(2) + 9 (Distribute)

9x + 27 = 9x + 18 + 9

9x + 27 = (9x) + ( 18 + 9)

(Combine Like Terms:)

9x + 27 = 9x + 27

9x + 27 = 9x + 27

Subtract 9x from both sides:

9x + 27 - 9x = 9x + 27 - 9x

27 = 27

Subtract 27 from both sides:

27 - 27 = 27 - 27

0 = 0

Equations is always true

Answer: All real numbers are solutions: (Infinitely many solutions:)

Hope that helps!!! ( Answer: Letter Choice (B), Infinitely many solutions.).

Answer 2

Let's solve the equation:

9x+27 = 9(x+2)+9 ← Distribute 9 to the x and 2

9x+27 = 9x+18+9 ← Combine like terms

9x+27 = 9x + 27 ← Subtract 27 from both sides

9x = 9x

Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.