We are asked to find out whether the given expressions are equivalent or not
Part A:
[tex]x+x+x+x\quad and\quad 4x[/tex]
These two expressions are equivalent since the sum of four individual x is equal to 4x.
[tex]x+x+x+x=4x[/tex]
For example:
Substitute x = 2
[tex]\begin{gathered} x+x+x+x\quad and\quad 4x \\ 2+2+2+2\quad and\quad 4(2) \\ 8\quad and\quad 8 \end{gathered}[/tex]
As you can see, the result of both expressions is equal therefore, these are equivalent expressions.
Part B:
[tex]5x\quad and\quad x+5[/tex]
These two expressions are not equivalent since, in the first expression, 5 is being multiplied with x and in the second expression 5 is being added to x.
[tex]5x\ne x+5[/tex]
For example:
Substitute x = 1
[tex]\begin{gathered} 5x\quad and\quad x+5 \\ 5(1)\quad and\quad 1+5 \\ 5\quad and\quad 6 \end{gathered}[/tex]
As you can see, the result of both expressions is not equal therefore, these are not equivalent.
