Question

name
for problems 1 - 4, distribute and combine like terms to write an equivalent expression. show your work.

1. $9 + 7(3x + 4)$
2. $\frac{1}{4}(4x + 40) - 6$
3. $2x + 3(4x - 8)$
4. $8(x + 3) + 5(2x + 6)$

Explanation:

Problem 1: \( 9 + 7(3x + 4) \)

Step 1: Distribute the 7

Using the distributive property \( a(b + c) = ab + ac \), we multiply 7 by each term inside the parentheses:
\( 7(3x + 4) = 7 \times 3x + 7 \times 4 = 21x + 28 \)
So the expression becomes \( 9 + 21x + 28 \)

Step 2: Combine like terms

The constant terms 9 and 28 can be combined:
\( 9 + 28 = 37 \)
So the simplified expression is \( 21x + 37 \)

Step 1: Distribute the \( \frac{1}{4} \)

Using the distributive property \( \frac{1}{4}(4x + 40) = \frac{1}{4} \times 4x + \frac{1}{4} \times 40 = x + 10 \)
So the expression becomes \( x + 10 - 6 \)

Step 2: Combine like terms

The constant terms 10 and -6 can be combined:
\( 10 - 6 = 4 \)
So the simplified expression is \( x + 4 \)

Step 1: Distribute the 3

Using the distributive property \( 3(4x - 8) = 3 \times 4x - 3 \times 8 = 12x - 24 \)
So the expression becomes \( 2x + 12x - 24 \)

Step 2: Combine like terms

The \( x \)-terms 2x and 12x can be combined:
\( 2x + 12x = 14x \)
So the simplified expression is \( 14x - 24 \)

Answer:

\( 21x + 37 \)

Problem 2: \( \frac{1}{4}(4x + 40) - 6 \)