Let's solve the equation \( 47 = 7 - 2(8 - 4x) \) for \( x \).

### Step 1: Simplify inside the parentheses
First, simplify the expression inside the parentheses:
\[
8 - 4x
\]

The equation becomes:
\[
47 = 7 - 2(8 - 4x)
\]

### Step 2: Distribute the \(-2\)
Next, distribute \(-2\) to both terms inside the parentheses:
\[
47 = 7 - 2 \times 8 + 2 \times 4x
\]
\[
47 = 7 - 16 + 8x
\]

### Step 3: Simplify the constant terms
Now simplify the constants on the right-hand side:
\[
47 = -9 + 8x
\]

### Step 4: Isolate the variable term
Add 9 to both sides of the equation to isolate the term with \( x \):
\[
47 + 9 = 8x
\]
\[
56 = 8x
\]

### Step 5: Solve for \( x \)
Divide both sides by 8 to solve for \( x \):
\[
x = \frac{56}{8}
\]
\[
x = 7
\]

Thus, the solution is \( x = 7 \).

Do you want further details or have any questions?

Here are 5 related questions to explore this concept:

1. How would the solution change if the coefficient of \(x\) was different?
2. What happens if the constant on the left side of the equation is altered?
3. Can you solve similar equations involving parentheses and distribution?
4. How do negative signs inside the parentheses affect the solution?
5. What is the process for checking if your solution is correct?

**Tip:** Always simplify expressions inside parentheses before distributing or combining like terms.

Explore how to solve the linear equation 47 = 7 - 2(8 - 4x) with a step-by-step solution. Learn how to apply the distributive property, isolate variables, and simplify expressions. This problem is suitable 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