Question

1. solve each equation, and explain or show your reasoning

a. ( a + 123 = 448 )
b. ( 2.5b = 26.5 )

Explanation:

Part a: Solve \( a + 123 = 468 \)

Step 1: Isolate \( a \)

To solve for \( a \), we subtract 123 from both sides of the equation. This is based on the subtraction property of equality, which states that if \( x = y \), then \( x - z = y - z \).
\[
a + 123 - 123 = 468 - 123
\]

Step 2: Simplify both sides

Simplifying the left side, \( a + 123 - 123 \) becomes \( a \). Simplifying the right side, \( 468 - 123 = 345 \).
\[
a = 345
\]

Step 1: Isolate \( b \)

To solve for \( b \), we divide both sides of the equation by 2.5. This is based on the division property of equality, which states that if \( x = y \), then \( \frac{x}{z}=\frac{y}{z} \) (where \( z
eq0 \)).
\[
\frac{2.5b}{2.5}=\frac{26.5}{2.5}
\]

Step 2: Simplify both sides

Simplifying the left side, \( \frac{2.5b}{2.5} \) becomes \( b \). Simplifying the right side, \( \frac{26.5}{2.5}=10.6 \).
\[
b = 10.6
\]

Answer:

\( a = 345 \)

Part b: Solve \( 2.5b = 26.5 \)