Write An Equivalent Expression For $h + 5 + 3 - 2h$.

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. One of the fundamental concepts in simplifying expressions is combining like terms. In this article, we will focus on simplifying the expression $h + 5 + 3 - 2h$ by combining like terms and rewriting it in an equivalent form.

Understanding Like Terms

Before we dive into simplifying the expression, let's understand what like terms are. Like terms are terms that have the same variable raised to the same power. In other words, they are terms that have the same algebraic structure. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Simplifying the Expression

Now that we understand like terms, let's simplify the expression $h + 5 + 3 - 2h$. To simplify this expression, we need to combine the like terms. The like terms in this expression are $h$ and $-2h$, which are both terms with the variable $h$ raised to the power of 1.

Combining Like Terms

To combine like terms, we add or subtract their coefficients. In this case, we have:

h+(−2h)=−hh + (-2h) = -h

So, the expression $h + (-2h)$ simplifies to $-h$.

Simplifying the Constant Terms

Now that we have simplified the like terms, let's simplify the constant terms. The constant terms in this expression are $5$ and $3$, which are both numbers.

Adding Constant Terms

To add constant terms, we simply add their values. In this case, we have:

5+3=85 + 3 = 8

So, the expression $5 + 3$ simplifies to $8$.

Combining the Simplified Terms

Now that we have simplified the like terms and the constant terms, let's combine them. We have:

−h+8-h + 8

This is the simplified expression.

Conclusion

In this article, we simplified the expression $h + 5 + 3 - 2h$ by combining like terms and rewriting it in an equivalent form. We started by understanding like terms and then simplified the expression by combining the like terms and adding the constant terms. The simplified expression is $-h + 8$.

Final Answer

The final answer is $\boxed{-h + 8}$.

Example Use Case

Here's an example use case for simplifying expressions:

Suppose we have the expression $2x + 3 + 4 - x$. To simplify this expression, we can follow the same steps as before:

  1. Identify the like terms: $2x$ and $-x$ are like terms because they both have the variable $x$ raised to the power of 1.
  2. Combine the like terms: $2x + (-x) = x$
  3. Simplify the constant terms: $3 + 4 = 7$
  4. Combine the simplified terms: $x + 7$

The simplified expression is $x + 7$.

Tips and Tricks

Here are some tips and tricks for simplifying expressions:

  • Always identify the like terms first.
  • Combine the like terms by adding or subtracting their coefficients.
  • Simplify the constant terms by adding or subtracting their values.
  • Combine the simplified terms to get the final expression.

By following these tips and tricks, you can simplify expressions like a pro!

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying expressions:

  • Not identifying the like terms.
  • Not combining the like terms correctly.
  • Not simplifying the constant terms.
  • Not combining the simplified terms correctly.

By avoiding these common mistakes, you can ensure that your simplified expressions are accurate and correct.

Frequently Asked Questions

Here are some frequently asked questions about simplifying expressions:

  • Q: What are like terms? A: Like terms are terms that have the same variable raised to the same power.
  • Q: How do I combine like terms? A: To combine like terms, add or subtract their coefficients.
  • Q: How do I simplify constant terms? A: To simplify constant terms, add or subtract their values.
  • Q: How do I combine simplified terms? A: To combine simplified terms, add or subtract their values.

By answering these frequently asked questions, you can clarify any doubts you may have about simplifying expressions.

Conclusion

In conclusion, simplifying expressions is a crucial skill that helps us solve equations and inequalities. By combining like terms and rewriting expressions in an equivalent form, we can simplify expressions like a pro! Remember to identify the like terms, combine them correctly, simplify the constant terms, and combine the simplified terms to get the final expression. By following these steps and avoiding common mistakes, you can simplify expressions with confidence and accuracy.