Question

identify the equation as a conditional equation, a contradiction, or an identity. then give the solution -3 + 2n = 2(n - 7) + 11
part 1 of 2
the equation is
a conditional equation.
a contradiction.
an identity.
part: 1 / 2
part 2 of 2
the solution set is

Explanation:

Part 1 of 2

Step 1: Simplify the right - hand side

First, we use the distributive property \(a(b + c)=ab+ac\) on the right - hand side of the equation \(-3 + 2n=2(n - 7)+11\).
For \(2(n - 7)\), we have \(2\times n-2\times7 = 2n-14\).
So the right - hand side becomes \(2n-14 + 11\).

Step 2: Combine like terms on the right - hand side

Combine \(-14\) and \(11\): \(2n-14 + 11=2n-3\).
Now our equation is \(-3 + 2n=2n-3\).
If we subtract \(2n\) from both sides, we get \(-3=-3\), which is a true statement for all values of \(n\). An equation that is true for all values of the variable is called an identity.

Since the equation \(-3 + 2n=2(n - 7)+11\) simplifies to a true statement (\(-3=-3\)) for all real numbers \(n\), the solution set includes all real numbers. In set - builder notation, the set of all real numbers is denoted by \(\mathbb{R}\).

Answer:

an identity

Part 2 of 2