Question

Check that 2b+b and 3b have the same value when b is 1,2, and 3. Do 2b+b and 3b have the same value for all values of b? Explain your reasoning

Answer 1

Expression 2b+b and 3b have same values for all values of b.

Explanation:

Given the two expression
`2b+b` and
`3b` and values of b as 1, 2 and 3.

Consider first expression that is,
`2b+b`.

Substituting the value of
`b=1`,

`2\left(1\right)+\left(1\right)=2+1=3` ....1

Substituting the value of
`b=2`,

`2\left(2\right)+\left(2\right)=4+2=6` ....2

Substituting the value of
`b=3`,

`2\left(3\right)+\left(3\right)=6+3=9` ....3

Consider second expression that is,
`3b`.

Substituting the value of
`b=1`,

`3\left(1\right)=3` ....4

Substituting the value of
`b=2`,

`3\left(2\right)=6` ....5

Substituting the value of
`b=3`,

`3\left(3\right)=9` ....6

For value of b=1, equation 1 and equation 4 are same, for value of b=2, equation 2 and equation 5 are same and for value of b=3 equation 3 and equation 6 are same.

Therefore both expression are same for all values of b.