Problem 70 - Prealgebra

Question

What number do you add to -7 to get 2?

Step-by-Step Solution

Answer

Add 9 to -7 to get 2.

Step 1: Understand the Equation

We need to find a number, let's call it \( x \), that when added to -7 gives a result of 2. This situation can be expressed using the equation: \(-7 + x = 2\).

Step 2: Isolate the Variable

To solve for \( x \), the variable, add 7 to both sides of the equation to isolate \( x \). This gives us: \(-7 + x + 7 = 2 + 7\).

Step 3: Simplify the Equation

On the left side, adding 7 and \(-7\) cancels each other, giving \( x \). On the right side, we calculate \( 2 + 7 \), which equals 9. Thus, the equation simplifies to: \( x = 9 \).

Key Concepts

Prealgebra Concepts

Prealgebra serves as the foundation for understanding basic mathematical operations and relationships. It covers the principles and skills necessary to deal with numbers and simple equations. Prealgebra typically involves operations like addition, subtraction, multiplication, and division, focusing on establishing mathematical literacy.

In the given problem, we are utilizing a basic algebraic equation to find an unknown value, represented as \( x \). Understanding how to manipulate equations—by performing the same operation on both sides—allows for the isolation and solution of \( x \). This method is a cornerstone in progressing to more advanced algebraic concepts.

Negative Numbers

Negative numbers are numbers less than zero and are indicated with a minus sign. In equations, negative numbers can be manipulated using operations similar to positive numbers, but care must be taken to adhere to the rules governing their use.

When adding a negative and a positive number, you are effectively subtracting the absolute value of the smaller number from the larger number's absolute value. For instance, the equation \(-7 + x = 2\) involves figuring out what value for \( x \) makes the sum equal 2. Dealing with this necessitates understanding how to manage negative values. In this context, adding 7 to both sides effectively cancels the negative 7, showing the importance of balancing the equation and understanding the role that negative numbers play.

Equation Solving Steps

Solving equations involves systematically progressing through a series of logical steps to find an unknown value. Here, solving for \( x \) is achieved through a clear process:

• Set up the equation: Start by expressing the problem with an equation, such as \(-7 + x = 2\).
• Isolate the variable: Perform operations to get the variable \( x \) by itself on one side of the equation. This often involves adding, subtracting, multiplying, or dividing both sides by the same number.
• Simplify: Once the variable is isolated, carry out the arithmetic on the other side of the equation to find the solution.

In this specific problem, you add 7 to both sides to isolate \( x \), resulting in the equation simplifying to \( x = 9 \). Understanding these steps is crucial because they are applicable across various algebraic problems, ensuring students build strong problem-solving skills.