Think about the equation 4(3x+2)=-16. Solve this equation by first distributing the multiplication by 4

Let's start by distributing the \(4\) to both terms inside the parentheses in the equation \(4(3x + 2) = -16\).

The equation becomes:

\[
4 \cdot 3x + 4 \cdot 2 = -16
\]

This simplifies to:

\[
12x + 8 = -16
\]

Next, we isolate the \(x\)-term by subtracting \(8\) from both sides of the equation:

\[
12x = -16 - 8
\]

This simplifies to:

\[
12x = -24
\]

Now, divide both sides of the equation by \(12\) to solve for \(x\):

\[
x = \frac{-24}{12} = -2
\]

Thus, the solution is:

\[
x = -2
\]

Would you like any further details on the steps?

Here are 5 related questions to expand on this problem:
1. What happens if you change the equation to \(4(3x + 5) = -16\)?
2. How would the solution change if the right-hand side was \( -20 \) instead of \( -16 \)?
3. Can you solve a similar equation like \(5(2x + 3) = 10\)?
4. What if you solve this equation with decimals instead, such as \(4(3.5x + 2.1) = -16\)?
5. What is the meaning of "distributing" in terms of algebraic operations?

**Tip**: Always distribute multiplication across addition/subtraction inside parentheses before solving the equation.

Think about the equation 4(3x+2)=-16. Solve this equation by first distributing the multiplication by 4.

Learn how to solve the linear equation 4(3x + 2) = -16 by distributing and isolating the variable step by step. This problem covers key algebra concepts like the distributive property and solving for x. Suitable for students in Grades 6-8.

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