Expressions and Equations

1. Apply the distributive property, then combine like terms:

$3(2x + 5) - 4x = 6x + 15 - 4x = 2x + 15$

2. The total cost is the registration fee plus the monthly charge times the number of months:

$C = 25 + 15m$

For $m = 8$:

$C = 25 + 15(8) = 25 + 120 = 145$

The total cost after 8 months is \145$.

3. Group like terms together:

$7a + 2a - 3b + 9b - 4 = 9a + 6b - 4$

4. Subtract 7 from both sides, then divide by 4:

$4x + 7 = 31$ $4x = 31 - 7$ $4x = 24$ $x = 6$

Check: $4(6) + 7 = 24 + 7 = 31$ ✓

5. The total cost is $8n + 16$, where $n$ is the number of books. This must be at most $120:

$8n + 16 \leq 120$ $8n \leq 104$ $n \leq 13$

The student can buy at most 13 books.