Subtract second from third: (9a + 3b + c) − (4a + 2b + c) = 2.5 − 1.8 → 5a + b = 0.7

February 22, 2026

Subtract Second from Third: Simplify (9a + 3b + c) − (4a + 2b + c) = 5.2 − 1.5 and Solve for a and b

Understanding how to subtract one algebraic expression from another and simplify complex equations is essential for mastering algebra. In this article, we’ll break down the expression: (9a + 3b + c) − (4a + 2b + c), simplify it step by step, and solve for the relationship between variables—specifically, how this leads to the equation 5a + b = 0.7.

Step 1: Understanding the Expression

We begin with: (9a + 3b + c) − (4a + 2b + c)

This involves subtracting a second expression from a first one. The second expression is fully enclosed in parentheses and has a negative sign before it, so this represents subtraction.

Step 2: Distribute the Subtraction Sign

Remember: subtracting inside parentheses changes the sign of each term: (9a + 3b + c) − 4a − 2b − c

Now expand fully: = 9a + 3b + c − 4a − 2b − c

Step 3: Combine Like Terms

Group and simplify terms containing the same variables:

For a: 9a − 4a = 5a
For b: 3b − 2b = 1b = b
For c: c − c = 0

After simplification: = 5a + b

So: (9a + 3b + c) − (4a + 2b + c) = 5a + b

Step 4: Match with the Right-Hand Side

The original problem states: (9a + 3b + c) − (4a + 2b + c) = 5.2 − 1.5 But 5.2 − 1.5 simplifies to 3.7, not 5.2 minus 1.8.

Wait — there’s a discrepancy. Let’s double-check the (9a + 3b + c) − (4a + 2b + c) simplification again.

Go back to: 5a + b — this simplifies to 5a + b = ?

Now compare to the problem’s result: It claims the result equals 0.7, but 5a + b = 0.7 implies: 5a + b = 0.7

So unless additional context or values for a and b are given, 5a + b must equal 0.7, not 3.7.

Where does 0.7 come from?

Possibility: You subtracted numbers incorrectly, or there’s a typo. The original subtraction yielded:

(9a + 3b + c) − (4a + 2b + c) = 5a + b But if someone incorrectly computes it and ends up with a number like 3.7, that suggests possibly: 9a + 3b + c − 4a + 2b − c = 5a + 5b = ? No — signs matter!

Wait! Rechecking carefully: (9a − 4a) + (3b − 2b) + (c − c) = 5a + b + 0 = 5a + b

This is correct.

Therefore, (9a + 3b + c) − (4a + 2b + c) simplifies uniquely to 5a + b.

Thus, the equation is: 5a + b = ?

But the problem says this equals 0.7, not 3.7. Unless:

The right side of the equation was miswritten, or
There’s missing context such as values for a and b.

Correct Interpretation & Final Simplification

Let’s state clearly: Step 1. Subtract expressions: (9a + 3b + c) − (4a + 2b + c) = 5a + b

Step 2. Compute the right-hand side numerically: 5.2 − 1.8 = 3.4, not 3.7. But if the expression led to 0.7, perhaps it was: (9a + 3b + c) − (4a + 2b + c) = 0.7

Then: 5a + b = 0.7

This makes sense. So likely, the 5.2 − 1.8 = 3.4 in the problem is a red herring or typo.

Best Practice for Subtracting Expr with Variables

To avoid confusion:

Always distribute the negative sign across all terms inside the second parentheses.
Combine like terms carefully.
Pay close attention to signs—especially when c or other variables appear.
After simplification, isolate the expression and compare with given constants.

Summary

(9a + 3b + c) − (4a + 2b + c) simplifies to 5a + b
No cancellation of intermediate constants like c removes terms cleanly if signs match
If conclusion is 5a + b = 0.7, then the right-hand side must be 0.7, not 3.4
Recheck problems for sign errors or mixed values

TL;DR

Subtract second from third: (9a + 3b + c) − (4a + 2b + c) = 5a + b

Simplified: 5a + b = ? If solution says 5a + b = 0.7, confirm constants. Ensure proper sign handling: don’t ignore signs when subtracting.

Key Takeaway: Master algebra by simplifying step-by-step — each term matters. Use consistent sign rules and confirm final expressions with given values to avoid common errors.

Keywords: subtract second from third, algebraic expression simplification, solve for a and b, 5a + b = 0.7, combine like terms, distribute negative signs in algebra, simplifying (9a + 3b + c) − (4a + 2b + c)

Meta Description: Learn how to simplify (9a + 3b + c) − (4a + 2b + c) to 5a + b using step-by-step algebraic rules. Understand how to solve and verify expressions equaling 0.7.