Question

lesson 4.4 cumulative practice for use before lesson 4.4 1. simplify \\( \frac{1}{5}(15x + 20) + 9x = \\) \\( \frac{1}{5}(15x + 20) + 9x = \underline{12x + 4} \\) 2. simplify \\( \frac{3}{5}(10x - 25) + 7x = \\) \\( \frac{3}{5}(10x - 25) + 7x = \underline{\quad\quad} \\)

Explanation:

Problem 1:

Step 1: Distribute the fraction

We use the distributive property \( \frac{1}{5}(15x + 20) = \frac{1}{5} \times 15x + \frac{1}{5} \times 20 \)
\( \frac{1}{5} \times 15x = 3x \), \( \frac{1}{5} \times 20 = 4 \)
So, \( \frac{1}{5}(15x + 20) = 3x + 4 \)

Step 2: Combine like terms

Now we add \( 9x \) to the result from step 1: \( 3x + 4 + 9x \)
Combine the \( x \)-terms: \( 3x + 9x = 12x \)
So, \( 3x + 4 + 9x = 12x + 4 \)

Step 1: Distribute the fraction

Using the distributive property \( \frac{3}{5}(10x - 25) = \frac{3}{5} \times 10x - \frac{3}{5} \times 25 \)
\( \frac{3}{5} \times 10x = 6x \), \( \frac{3}{5} \times 25 = 15 \)
So, \( \frac{3}{5}(10x - 25) = 6x - 15 \)

Step 2: Combine like terms

Now we add \( 7x \) to the result from step 1: \( 6x - 15 + 7x \)
Combine the \( x \)-terms: \( 6x + 7x = 13x \)
So, \( 6x - 15 + 7x = 13x - 15 \)

Answer:

\( 12x + 4 \)

Problem 2: