Problem 92 - Elementary Algebra

Question

Problem: Simplify: \(4-(x+9)\) Incorrect Answer: \(4-(x+9)\) $$ \begin{aligned} &=4-x+9 \\ &=-x+13 \end{aligned} $$

Step-by-Step Solution

Answer

-x - 5

Step 1: Identify the problem

The problem requires simplifying the expression: \(4-(x+9)\)

Step 2: Distribute the negative sign

Distribute the negative sign inside the parentheses: \( -(x+9) = -x-9 \). Therefore, the expression becomes: \[ 4 - (x + 9) = 4 - x - 9 \]

Step 3: Combine like terms

Combine the constant terms: \[ 4 - 9 = -5 \]. So the expression now is: \[ -x - 5 \]

Key Concepts

Distributing Negative Signs

One key step in simplifying algebraic expressions is distributing negative signs. When a negative sign is placed in front of a parenthesis, it must be applied to each term inside. For example:

\(4-(x+9)\) requires us to distribute the negative sign to both \(x\) and \(9\). This means that we change the signs of each term:

\[ -(x+9) = -x -9 \]

Now, the expression becomes \[4 - x - 9\]. This step is critical because forgetting to distribute a negative sign can lead to incorrect answers. Always ensure you apply the negative sign to each term inside the parentheses.

Combining Like Terms

Combining like terms is the next essential step in simplifying algebraic expressions. Like terms have the same variable raised to the same power. You can combine these terms by adding or subtracting their coefficients.

For instance, after distributing the negative sign in the problem \[4-(x+9)\] we get \[4 - x - 9\].

Now, look for like terms to combine. Here, \4\ and \-9\ are constants, and they can be combined:

\4 - 9 = -5\

Therefore, the final simplified expression is:

\ -x - 5 \ .

This process helps in reducing complex expressions into simpler forms, making it easier to understand and solve algebraic problems.

Elementary Algebra

Elementary algebra includes understanding and applying basic algebraic rules to simplify expressions and solve equations. Simplifying expressions often involves:

• Identifying and distributing signs.
• Combining like terms.
• Reordering terms for simplicity.

All these steps were demonstrated in the problem \[4 - (x + 9)\]. By first distributing the negative sign and then combining like terms, we simplified it to \ -x - 5 \.
These skills form the foundation for more advanced algebraic concepts and are crucial for solving more complex equations. Practice these steps regularly to gain confidence and proficiency in elementary algebra.