Let's solve the equation step by step:

### Given equation:
\[
4(3x + 2) - 2x - 3 = -15
\]

### Step 1: Expand the terms
Distribute the \(4\) over the terms inside the parentheses:
\[
4(3x + 2) = 12x + 8
\]
So the equation becomes:
\[
12x + 8 - 2x - 3 = -15
\]

### Step 2: Combine like terms
Combine the \(x\)-terms and constant terms on the left-hand side:
\[
(12x - 2x) + (8 - 3) = 10x + 5
\]
Now the equation is:
\[
10x + 5 = -15
\]

### Step 3: Isolate the variable \(x\)
First, subtract 5 from both sides:
\[
10x = -15 - 5
\]
\[
10x = -20
\]

Now, divide both sides by 10 to solve for \(x\):
\[
x = \frac{-20}{10}
\]
\[
x = -2
\]

### Final answer:
\[
x = -2
\]

Let me know if you'd like further details!

---

Here are some related questions to explore:
1. How would the solution change if the constant term on the right side was different?
2. What happens when we introduce an additional variable in the equation?
3. How can you check if your solution for \(x\) is correct?
4. What if the equation had fractions? How would you approach that?
5. How can we graphically interpret the solution of this equation?

**Tip:** Always double-check your solution by plugging it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation 4(3x + 2) − 2x − 3 = -15 with a step-by-step solution. This problem involves key algebraic concepts like the distributive property and combining like terms. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation