Question

directions: simplify each expression.

1. $5(x + 4) + 9$
2. $7 + 9(2 + k)$
3. $-4(w + 7) - w$
4. $8a - 2(a - 7)$

Explanation:

Problem 9: Simplify \( 5(x + 4) + 9 \)

Step 1: Distribute the 5

Using the distributive property \( a(b + c) = ab + ac \), we have:
\( 5(x + 4) = 5x + 5 \times 4 = 5x + 20 \)

Step 2: Combine like terms

Now add 9 to \( 5x + 20 \):
\( 5x + 20 + 9 = 5x + 29 \)

Step 1: Distribute the 9

Using the distributive property \( a(b + c) = ab + ac \), we get:
\( 9(2 + k) = 9 \times 2 + 9k = 18 + 9k \)

Step 2: Combine like terms

Add 7 to \( 18 + 9k \):
\( 7 + 18 + 9k = 25 + 9k \) (or \( 9k + 25 \))

Step 1: Distribute the -4

Using the distributive property \( a(b + c) = ab + ac \), we have:
\( -4(w + 7) = -4w - 4 \times 7 = -4w - 28 \)

Step 2: Combine like terms

Subtract \( w \) (which is the same as adding \( -w \)) to \( -4w - 28 \):
\( -4w - 28 - w = (-4w - w) - 28 = -5w - 28 \)

Answer:

\( 5x + 29 \)

Problem 10: Simplify \( 7 + 9(2 + k) \)