Question

Decide if the expression in each pair of equivalent explain how you know A.x+x+x+x and 4x

Answer 1

We are asked to find out whether the given expressions are equivalent or not

Part A:

`x+x+x+x\quad and\quad 4x`

These two expressions are equivalent since the sum of four individual x is equal to 4x.

`x+x+x+x=4x`

For example:

Substitute x = 2

`\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}`

As you can see, the result of both expressions is equal therefore, these are equivalent expressions.

Part B:

`5x\quad and\quad x+5`

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.

`5x\\e x+5`

For example:

Substitute x = 1

`\begin{gathered} 5x\quad and\quad x+5 \\ 5(1)\quad and\quad 1+5 \\ 5\quad and\quad 6 \end{gathered}`

As you can see, the result of both expressions is not equal therefore, these are not equivalent.