Simplifying the Expression: -22x – 14 + 14x – How to Combine Like Terms (Step-by-Step)

Understanding algebraic expressions is fundamental in mastering high school and early college mathematics. One common task students face is simplifying linear expressions like -22x – 14 + 14x. Whether you're solving equations, graphing functions, or working with variables, simplifying expressions makes them easier to analyze and solve.

In this article, we’ll break down the expression -22x – 14 + 14x step by step to show exactly how to combine like terms — a key algebra skill that improves clarity and accuracy in math work.

Understanding the Context

What Is the Expression We’re Simplifying?

We begin with the expression:
-22x – 14 + 14x

This expression contains three terms:

  • -22x: a linear term with coefficient -22
  • –14: a constant (numerical) term
  • +14x: another linear term with coefficient +14
= -22x -14 + 14x

Key Insights

Step 1: Identify Like Terms

To simplify, we must combine like terms — terms that contain the same variable raised to the same power.

  • Like terms with x: -22x and +14x
  • Non-like term: –14 (a constant, no variable)

So, only -22x and 14x are like terms and can be combined.

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Thus, the probability is \(\boxed{\frac{1}{4}}\).
Question:** Suppose that \( v \) is a positive multiple of 5. If \( v^2 \) is less than 600, what is the greatest possible value of \( v \)?
We are given that \( v \) is a positive multiple of 5, and \( v^2 < 600 \).

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Final Thoughts

Step 2: Combine the x Terms

Add the coefficients of the like terms:

-22x + 14x = (–22 + 14)x = –8x

Step 3: Include the Constant Term

Now replace the x terms and include the constant:

–8x – 14

This is the simplified form.