Let's solve the equation step by step:

Given equation:
\[
74(x - 4) = 32(x + 2)
\]

### Step 1: Distribute on both sides.
Distribute 74 on the left-hand side:
\[
74(x - 4) = 74x - 296
\]

Distribute 32 on the right-hand side:
\[
32(x + 2) = 32x + 64
\]

So the equation now is:
\[
74x - 296 = 32x + 64
\]

### Step 2: Isolate the variable \(x\).
Subtract \(32x\) from both sides:
\[
74x - 32x - 296 = 64
\]
Simplify:
\[
42x - 296 = 64
\]

### Step 3: Move the constant term to the other side.
Add 296 to both sides:
\[
42x = 64 + 296
\]
\[
42x = 360
\]

### Step 4: Solve for \(x\).
Divide both sides by 42:
\[
x = \frac{360}{42}
\]

Simplify the fraction:
\[
x = \frac{360 \div 6}{42 \div 6} = \frac{60}{7}
\]

### Final Answer:
\[
x = \frac{60}{7} \approx 8.57
\]

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How would you solve \(84(x - 3) = 48(x + 1)\)?
2. What if the equation had been \(50(x - 2) = 20(x + 3)\)?
3. How can you solve an equation with decimals, like \(3.5(x - 1.2) = 1.8(x + 0.4)\)?
4. How do you check the solution of an equation?
5. What if the equation had been \(74(x + 4) = 32(x - 2)\)?
6. How can you solve for \(x\) in a quadratic equation like \(x^2 + 4x - 3 = 0\)?
7. How does distributing work when the equation has fractions, like \(\frac{5}{2}(x - 4) = \frac{3}{2}(x + 6)\)?
8. What is the difference between a linear and a quadratic equation?

**Tip:** When solving equations, always simplify the equation as much as possible before isolating the variable \(x\).

Learn how to solve the equation 74(x-4)=32(x+2) step-by-step with detailed explanations. This problem involves equations with variables on both sides and includes distribution and simplification techniques. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation