Problem 43 - Prealgebra

Question

Find the value of \(2 x+6\) when \(x=-2\)

Step-by-Step Solution

Answer

The value of the expression is 2 when \(x = -2\).

Step 1: Substitute the Given Value

First, we need to substitute the given value of \(x\) into the expression \(2x + 6\). Here, \(x = -2\). So, replace \(x\) with \(-2\):\[2(-2) + 6\]

Step 2: Perform Multiplication

Next, perform the multiplication in the expression. Multiply \(2\) by \(-2\):\[2(-2) = -4\]Thus, the expression becomes:\[-4 + 6\]

Step 3: Perform Addition

Now, add the results of the multiplication to the constant number in the expression:\[-4 + 6 = 2\]Therefore, the value of the expression \(2x + 6\) when \(x = -2\) is \(2\).

Key Concepts

Substitution

Substitution is a simple yet powerful concept in algebra. It involves replacing a variable with a specific value. In the given exercise, the expression is \(2x + 6\). Here, the variable is \(x\).
When we substitute \(-2\) for \(x\), the expression becomes \(2(-2) + 6\). This process allows us to evaluate the expression by using the provided value for \(x\).

• Write down the expression clearly.
• Identify the variable you need to substitute.
• Replace the variable with the given number.

Substitution makes complex expressions more manageable by eliminating variables and helping us focus on arithmetic operations.

Multiplication

Multiplication is one of the basic operations in arithmetic. After substituting \(-2\) for \(x\) in the expression, the next step is multiplication. This involves multiplying \(2\) by \(-2\), which gives us \(-4\).
Here's how it works:

• Identify the coefficients and numbers to be multiplied.
• Apply the multiplication operation: \(2 \times -2 = -4\).
• Remember that multiplying a positive number by a negative number results in a negative product.

Multiplying effectively simplifies the expression, making it easier to add the remaining terms, which is the next step in solving the problem.

Addition

In mathematics, addition is used to find the total sum of numbers. After completing the substitution and multiplication steps, the problem simplifies to \(-4 + 6\). Now it's time to perform the addition.
To do this, follow these steps:

• Align the terms for easy calculation, starting with the negative number.
• Combine the terms: Adding \(-4\) and \(+6\) equals \(+2\).
• Understand that this step often checks your signs knowledge - positive and negative.

Addition is critical for arriving at the final result. It concludes the problem-solving process by providing the simplified answer: In our case, the value of the expression is \(2\) when \(x = -2\).