Answer: (D) all real numbers
Step-by-step explanation:
4(a + 3) = 12 + 4a
4a + 12 = 12 + 4a distributed 4 into a + 3
12 = 12 subtracted 4a from both sides
TRUE
A true statement means they are the same equation so any value you plug in for "a" will make a true statement. There are an infinite number of solutions.
Examples:
Let a = 0, then 4(0 + 3) = 12 + 4(0)
⇒ 4(3) = 12 + 0
⇒ 12 = 12
Let a = 10, then 4(10 + 3) = 12 + 4(10)
⇒ 4(13) = 12 + 40
⇒ 52 = 52
Let a = 100, then 4(100 + 3) = 12 + 4(100)
⇒ 4(103) = 12 + 400
⇒ 412 = 412
Any number you choose, will make a true statement so the solution is "all real numbers".
