 4x + 2(x – 2) (x – 3) = (x – 4) · 2(x – 1)

Let's solve the equation step by step:

Given:
\[
4x + 2(x - 2)(x - 3) = (x - 4) \cdot 2(x - 1)
\]

### Step 1: Expand both sides

#### Left-hand side:
\[
4x + 2(x - 2)(x - 3)
\]
First, expand \( (x - 2)(x - 3) \):
\[
(x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6
\]
Now multiply by 2:
\[
2(x^2 - 5x + 6) = 2x^2 - 10x + 12
\]
Thus, the left-hand side becomes:
\[
4x + 2x^2 - 10x + 12 = 2x^2 - 6x + 12
\]

#### Right-hand side:
\[
(x - 4) \cdot 2(x - 1)
\]
First, expand \( (x - 4)(x - 1) \):
\[
(x - 4)(x - 1) = x^2 - x - 4x + 4 = x^2 - 5x + 4
\]
Now multiply by 2:
\[
2(x^2 - 5x + 4) = 2x^2 - 10x + 8
\]
Thus, the right-hand side becomes:
\[
2x^2 - 10x + 8
\]

### Step 2: Set up the equation
Now we have:
\[
2x^2 - 6x + 12 = 2x^2 - 10x + 8
\]

### Step 3: Eliminate common terms
Subtract \( 2x^2 \) from both sides:
\[
-6x + 12 = -10x + 8
\]

### Step 4: Solve for \( x \)
Move all terms involving \( x \) to one side:
\[
-6x + 10x = 8 - 12
\]
\[
4x = -4
\]

Now solve for \( x \):
\[
x = -1
\]

### Solution:
The solution to the equation is \( x = -1 \).

Would you like more details or have any questions?

Here are five related questions you can try:
1. Solve: \( 3x + (x - 1)(x - 2) = 2(x - 3) \)
2. Solve: \( 5x + 2(x - 1)(x + 2) = 4x(x - 3) \)
3. Expand and simplify: \( (x - 3)(x + 4) + (x - 1)^2 \)
4. Solve: \( (x - 2)^2 = 4(x + 1) \)
5. Factor: \( 2x^2 - 6x + 4 \)

**Tip:** Always distribute and combine like terms carefully when solving equations involving parentheses.

4x + 2(x – 2)(x – 3) = (x – 4) · 2(x – 1)

Explore how to solve the polynomial equation 4x + 2(x – 2)(x – 3) = (x – 4) · 2(x – 1) with a comprehensive, step-by-step breakdown. This solution covers polynomial expansion, the distributive property, and the principles of solving equations, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation