Simplify the equation 48x + 32x = 320 by combining like terms. What is the value of x?

Introduction:
This question checks basic algebra: combining like terms and solving a linear equation. Terms like 48x and 32x are “like terms” because both contain x to the same power (x^1). You add their coefficients, then isolate x by dividing both sides by the combined coefficient. This is a foundational simplification skill used in equations, inequalities, and word problems.

Given Data / Assumptions:

• Equation: 48x + 32x = 320
• x is a real number
• Like terms can be combined by adding coefficients

Concept / Approach:
Combine the x-terms first: (48 + 32)x. Then solve (80x = 320) by dividing both sides by 80. This keeps the work clean and prevents arithmetic mistakes.

Step-by-Step Solution:
48x + 32x = (48 + 32)x = 80x So the equation becomes 80x = 320 Divide both sides by 80: x = 320/80 x = 4

Verification / Alternative check:
Substitute x = 4 into the original equation: 48*4 + 32*4 = 192 + 128 = 320. The left side equals the right side, so x = 4 is correct.

Why Other Options Are Wrong:
If x = 8, left side becomes 640. If x = 16, it becomes 1280. If x = 32, it becomes 2560. If x = 2, it becomes 160. Only x = 4 satisfies the equation exactly.

Common Pitfalls:
Adding 48 and 32 incorrectly, or dividing by the wrong coefficient after combining like terms.

Final Answer:
The value of x is 4.