Solving (5a + b) − (3a + b) = 0.7 − 0.6: Step-by-Step Explanation Behind 2a = 0.1 → a = 0.05

Understanding basic algebra can transform how you solve equations—especially when simplifying expressions with variables. One clear example is solving the equation:
(5a + b) − (3a + b) = 0.7 − 0.6
But why equal 0.1 and how does this lead to a = 0.05? Let’s break it down step-by-step.

Understanding the Context

Step 1: Simplify the Left Side of the Equation

Start by simplifying the left-hand side:
(5a + b) − (3a + b)
Distribute the negative sign:
= 5a + b − 3a − b
Now combine like terms:
(5a − 3a) + (b − b) = 2a + 0 = 2a

So:
(5a + b) − (3a + b) = 2a

Step 2: Simplify the Right Side

Evaluate the right-hand side:
0.7 − 0.6 = 0.1

Now subtract: (5a + b) − (3a + b) = 0.7 − 0.6 → 2a = 0.1 → a = 0.05

Key Insights

Now the equation becomes:
2a = 0.1

Step 3: Isolate Variable a

To solve for a, divide both sides by 2:
2a ÷ 2 = 0.1 ÷ 2
→ a = 0.05

Why Does This Work?

The key simplifications come from removing the parentheses and canceling the +b terms. Subtracting identical terms (like b − b) eliminates them, simplifying expressions and clearly revealing the variable relationship. The arithmetic shows how consistent terms on both sides allow clean algebraic manipulation.

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Therefore, the number of distinct sequences is $ \boxed{1260} $.Question: A technology consultant models data flow efficiency using the function $ f(\theta) = \sin^4 \theta - 4\sin^2 \theta \cos^2 \theta + \cos^4 \theta $. Find the minimum value of $ f(\theta) $ over all real $ \theta $.
Solution: We begin by rewriting $ f(\theta) $ using trigonometric identities. Observe:
f(\theta) = \sin^4 \theta - 4\sin^2 \theta \cos^2 \theta + \cos^4 \theta.

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Final Thoughts

Real-World Application

Solving equations like this helps in many everyday and technical contexts—from budgeting and physics to programming and finance. Mastering this step-by-step method strengthens your problem-solving foundation.

Summary

Given:
(5a + b) − (3a + b) = 0.7 − 0.6
→ 2a = 0.1
→ a = 0.05

This simple subtraction and cancellation process demonstrates how algebra decodes linear relationships—making it easier to find unknowns like a safely and confidently.

If you’re learning algebra or want to sharpen your skills, practice combining like terms and simplifying both sides carefully. With these techniques, equations like this become quick and straightforward!