Answer:
None of them
Step-by-step explanation:
In an identity, the left-hand side must equal the right-hand side for all values of x.
We will have to test each equation.
A.
[tex]\begin{array}{rcl}3(x - 1)& =& x + 2(x + 1) + 1\\3x - 3 & = & x + 2x + 2 +1\\3x - 3 & = & 3x + 3\\-3 & \neq &3\\\end{array}\\[/tex]
[tex]\text{The equation is }\textbf{not}\text{ an identity}[/tex]
B.
[tex]\begin{array}{rcl}2 - 4(x + 1)& =& -3(x + 1) + 1\\2 -4x - 4 & =&-3x - 3 + 1\\-4x - 2 & = &-3x - 2\\-4x & \neq &3x\\\end{array}\\\text{The equation is }\textbf{not}\text{ an identity}[/tex]
C.
[tex]\begin{array}{rcl}21+ 3& = &1(4x + 2) + 2\\24& =& 4x + 2 + 1\\24 & =&4x+ 3\\21 & = &4x \\\end{array}\\\text{The equation is }\textbf{not}\text{ an identity}[/tex]
D.
[tex]\begin{array}{rcl}6x - 3 &=& 3(x + 1) - x - 2\\6x - 3& = &3x + 3 - x - 2\\6x -3 & = & 2x + 1\\4x -3 & = & 1\\x & = & 4\\\end{array}\\\text{The equation is }\textbf{not}\text{ an identity}[/tex]
