To solve the equation \( 0.4(p + 5) - 0.9(p + 4) = -4 \), we will distribute the constants inside the parentheses, combine like terms, and solve for \( p \).

### Step 1: Distribute the constants
Distribute \( 0.4 \) and \( -0.9 \) to the terms inside the parentheses:

\[
0.4(p + 5) = 0.4p + 2
\]
\[
-0.9(p + 4) = -0.9p - 3.6
\]

Now the equation becomes:
\[
0.4p + 2 - 0.9p - 3.6 = -4
\]

### Step 2: Combine like terms
Combine the \( p \)-terms and the constant terms:

\[
(0.4p - 0.9p) + (2 - 3.6) = -4
\]
\[
-0.5p - 1.6 = -4
\]

### Step 3: Isolate the variable \( p \)
Add \( 1.6 \) to both sides to isolate the \( p \)-term:

\[
-0.5p = -4 + 1.6
\]
\[
-0.5p = -2.4
\]

### Step 4: Solve for \( p \)
Divide both sides by \( -0.5 \):

\[
p = \frac{-2.4}{-0.5} = 4.8
\]

Thus, the solution is:
\[
p = 4.8
\]

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the solution to \( 0.3(p + 4) - 0.7(p + 5) = -3 \)?
2. How do you solve equations with distribution and combining like terms?
3. What happens if the equation was \( 0.5(p - 2) - 0.3(p + 6) = -5 \)?
4. How do you solve an equation involving decimals and fractions simultaneously?
5. How do you check if the solution to an equation is correct?

**Tip:** When solving equations, always distribute and combine like terms before isolating the variable to avoid mistakes.

Learn how to solve the equation 0.4(p + 5) - 0.9(p + 4) = -4 with a detailed step-by-step solution. This problem involves distributing constants, combining like terms, and isolating variables. Suitable for Grades 7-9 students learning about equations and algebraic manipulation.

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