= -22x -14 + 14x
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.
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
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.
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.
Final Simplified Expression
-8x – 14
This expression is fully simplified — only one linear term and one constant remain.
Why Simplifying Matters
Simplifying algebraic expressions helps in multiple ways:
- Makes solving equations easier (e.g., when setting the expression equal to zero)
- Clarifies graphing behavior (linear functions in slope-intercept form)
- Reduces complexity in more advanced math, such as calculus and algebraic manipulation
Summary
Simplifying -22x – 14 + 14x follows these clear algebra steps:
- Identify like terms (only –22x and +14x)
- Combine coefficients: –22 + 14 = –8
- Keep constants unchanged
- Write the simplified result: -8x – 14
Mastering this process builds a strong foundation in algebra — essential for any student aiming to excel in math.
Want to practice more? Try simplifying other expressions like:
3x + 5 – 2x – 7 –5y + 3y + 9 – 4 or complex multi-step equations with variables on both sides.
With consistent practice, algebraic simplification becomes second nature — paving your way to higher-level math success!
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