Question

What value of y would make the expression yb - 6+ 7 + 2b - 3b + 1 equivalent to 5b + 2?

Answer 1

To find the value of \( y \) that makes the expression \( yb - 6 + 7 + 2b - 3b + 1 \) equivalent to \( 5b + 2 \), we simplify the left-hand side first:

Start with the original expression:

\[
yb - 6 + 7 + 2b - 3b + 1
\]

Now combine like terms:

1. Combine the constant terms:

\[
-6 + 7 + 1 = 2
\]

2. Combine the \( b \) terms:

\[
yb + 2b - 3b = (y + 2 - 3)b = (y - 1)b
\]

Putting it all together, we get:

\[
(y - 1)b + 2
\]

Next, we set this equal to the right-hand side, \( 5b + 2 \):

\[
(y - 1)b + 2 = 5b + 2
\]

To solve for \( y \), we can first subtract 2 from both sides:

\[
(y - 1)b = 5b
\]

Next, we can factor out \( b \) from both sides, assuming \( b \neq 0 \):

\[
y - 1 = 5
\]

Now solve for \( y \):

\[
y = 5 + 1
\]

\[
y = 6
\]

Thus, the value of \( y \) that makes the expression equivalent to \( 5b + 2 \) is

\[
\boxed{6}
\]