Simplify: $h+3 c-2-6 h+4 c$
Answer (1)
Group like terms: ( h − 6 h ) + ( 3 c + 4 c ) − 2 .
Combine the 'h' terms: h − 6 h = − 5 h .
Combine the 'c' terms: 3 c + 4 c = 7 c .
The simplified expression is − 5 h + 7 c − 2 .
Explanation
Understanding the Expression We are given the expression h + 3 c − 2 − 6 h + 4 c and our goal is to simplify it by combining like terms. Like terms are those that contain the same variable raised to the same power. In this case, we have terms with h , terms with c , and constant terms.
Grouping Like Terms First, let's group the like terms together: ( h − 6 h ) + ( 3 c + 4 c ) − 2 .
Combining 'h' Terms Now, let's combine the terms with h : 1 h − 6 h = − 5 h .
Combining 'c' Terms Next, let's combine the terms with c : 3 c + 4 c = 7 c .
Identifying the Constant Term Finally, we have the constant term, which is − 2 .
Writing the Simplified Expression Putting it all together, the simplified expression is − 5 h + 7 c − 2 .
Final Answer Therefore, the simplified form of the given expression is − 5 h + 7 c − 2 .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics and has numerous real-world applications. For example, imagine you are planning a party and need to calculate the total cost. You might have a fixed cost for the venue and variable costs depending on the number of guests. If you represent the number of guests with a variable, you can use algebraic expressions to model the total cost. Simplifying such expressions helps you quickly determine the cost for different numbers of guests, making budgeting and planning easier. This skill is also crucial in fields like engineering, physics, and economics, where complex relationships are often modeled using algebraic equations.
