Problem 42 - Algebra 1

Question

Evaluate the expression. \(-8 x\) when \(x=6\)

Step-by-Step Solution

Answer

The value of the given expression \(-8 x\) when \(x=6\) is \(-48\).

Step 1: Substitute

Firstly, replace the variable \(x\) in the expression \(-8x\) with the value that has been given, which is 6. This will result in the expression turning into \(-8(6)\).

Step 2: Simplify

Now after substituting, the expression becomes \(-8*6\). Multiply it which gives \(-48\).

Key Concepts

Substitution Method

The substitution method is essential when you have variable expressions. It's about replacing variables with provided specific values to simplify problems or evaluate expressions. Here's how it works:

• Identify the variable in the expression. In our case, that's "x" in the expression \(-8x\).
• Find the value you're asked to substitute for the variable. Here, it's given as 6.
• Substitute the value into the expression wherever the variable appears. Replace "x" with 6 in the expression, resulting in \(-8(6)\).

By carrying out these steps, you change a variable expression into a numerical one, making it much easier to work with.

Multiplication with Integers

Multiplying integers is a key mathematical skill. Here, you need to understand not just the arithmetic operations, but also how signs affect the result.

• When multiplying integers with the same sign (both positive or both negative), the result is positive. For example, \(4 imes 5 = 20\) or \(-4 \times -5 = 20\).
• When they have different signs (one positive, one negative), the result is negative. For instance, \(-8 \times 6 = -48\).

In our exercise, the integers are \(-8\) and 6. Since \(-8\) is negative and 6 is positive, multiplying them yields a negative result, which is \(-48\). Understanding these rules ensures accurate computations when dealing with integer operations.

Simplifying Expressions

Once you've substituted variables and performed operations, simplifying is often the last step to make the expression as straightforward as possible. Here's how you do it:

• Complete the arithmetic operations, while following the correct order: parenthesis, exponents, multiplication and division, addition, and subtraction (PEMDAS).
• Ensure that there are no further operations that can simplify the expression further.

In the activity we performed, after substituting \(x=6\) into \(-8x\), we multiplied to simplify, resulting in \(-48\). There were no further operations needed, so this was our final simplified expression. Simplifying makes expressions cleaner, often serving as a valuable skill in both math problems and real-world applications.