Question

Solve the equation. Check your answer.
bminus5plus7bequals24

Answer 1

To solve the equation \( b - 5 + 7b = 24 \), we can first combine like terms.

Combine \( b \) and \( 7b \):

\[
b + 7b = 8b
\]

Now, rewrite the equation:

\[
8b - 5 = 24
\]

Next, add 5 to both sides:

\[
8b - 5 + 5 = 24 + 5
\]

This simplifies to:

\[
8b = 29
\]

Now, divide both sides by 8:

\[
b = \frac{29}{8}
\]

Now we can check our solution by substituting \( b = \frac{29}{8} \) back into the original equation:

Starting with the left side of the equation:

\[
b - 5 + 7b = \frac{29}{8} - 5 + 7 \cdot \frac{29}{8}
\]

First, compute \( 5 \) in terms of eighths:

\[
5 = \frac{40}{8}
\]

Now substitute:

\[
\frac{29}{8} - \frac{40}{8} + 7 \cdot \frac{29}{8}
\]

Calculate \( \frac{29}{8} - \frac{40}{8} \):

\[
\frac{29 - 40}{8} = \frac{-11}{8}
\]

Now calculate \( 7 \cdot \frac{29}{8} \):

\[
\frac{203}{8}
\]

Now combine \( -\frac{11}{8} \) and \( \frac{203}{8} \):

\[
-\frac{11}{8} + \frac{203}{8} = \frac{-11 + 203}{8} = \frac{192}{8} = 24
\]

Since the left-hand side equals 24, our solution is verified:

\[
b = \frac{29}{8}
\] is the correct answer.