Question

Two equivalent expressions are shown in the equation where a and b are both integers. a(7x+ 3) = b + 14x What are the values of a and b?The value of a is...The value of b is...

Answer 1

`\begin{gathered} a(7x+3)\equiv b+14x \\ \text{Use distributive property on the left hand side:} \\ 7xa+3a=b+14x \\ \end{gathered}`

They are equivalent, so, equating the coefficients of the polynomial:

`\begin{gathered} 7a=14 \\ so\colon \\ a=(14)/(7) \\ a=2 \\ ----- \\ 3a=b \\ so\colon \\ 3(2)=b \\ b=6 \end{gathered}`