Problem 21 - Elementary Algebra

Question

Evaluate. \(-x+12,\) where \(x=-2\)

Step-by-Step Solution

Answer

The value of the expression is 14.

Step 1: Substitute the Value of x

First, replace the variable \(x\) with the given value of \(x = -2\) in the expression \(-x + 12\). This gives us \(-(-2) + 12\).

Step 2: Simplify the Expression

Next, simplify the expression. \(-(-2)\) is equal to \(+2\), so the expression becomes \(2 + 12\).

Step 3: Evaluate the Sum

Finally, add the numbers together: \(2 + 12 = 14\).

Key Concepts

Substitution Method

In algebra, the substitution method is used to solve expressions and equations by replacing variables with numbers. Think of it as swapping out the letter for the number it represents. This helps you work with numbers alone, making it easier to simplify and solve.
To substitute correctly, you’ll want to follow these steps:

• Identify the variable in your expression or equation. Here, that variable is "x."
• Replace the variable with the number given. In our case, we replace "x" with "-2."

Once the variable is replaced, the expression typically becomes simpler to work with, as it did when we turned \(-x + 12\) into \(-(-2) + 12\). This is a crucial first step to solving or evaluating algebraic expressions effectively.

Simplification

Simplification involves reducing an expression to its simplest form. This process makes our math tasks easier to handle and helps us reach the final answer faster. After substituting variables, our goal is to simplify the expression so it's easy to solve.
For example, in the expression \(-(-2) + 12\), we simplify \(-(-2)\). Double negatives in math, as in language, can be confusing, but they actually cancel each other out. So \(-(-2)\) becomes \(+2\).
After simplifying the negative portions, combine any numbers left in the expression. Now we have \(2 + 12\). This is much simpler than our original expression, and we can clearly see where our final operations will take us.

Negative Numbers

Negative numbers are intriguing yet sometimes tricky. They are simply numbers less than zero, labeled with a minus sign. Understanding how they operate is crucial, especially in algebra.

• When you substitute a negative number into an expression, it's vital to keep track of the minus signs. This ensures accuracy in any further steps like simplification.
• A double negative, as seen in \(-(-2)\), means you flip the sign to positive. It's as though two negatives make a positive!

Negative numbers may change the way you add or subtract, as seen in our example. \(+2\) and \(+12\) easily add up to \(14\), but starting with negatives requires special attention to avoid mistakes.