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

Answer:

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

Step-by-step 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.