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Magazine Chapter 2: Problem 68
What number do you add to -5 to get -8?
Short Answer
Expert verified
Add -3 to -5 to get -8.
Step by step solution
01
Understanding the Problem
We are asked to find a number that, when added to -5, results in -8. Let's denote this unknown number as \( x \).
02
Setting Up the Equation
To express the problem mathematically, we can write the equation: \(-5 + x = -8\). The goal is to find the value of \( x \).
03
Isolating the Variable
To solve for \( x \), we need to isolate it. We can do this by subtracting \(-5\) from both sides of the equation to get: \( x = -8 + 5 \).
04
Solving the Equation
Now calculate \(-8 + 5\). This addition results in: \(-3\). Hence, \( x = -3 \).
05
Verification
To verify our solution, add \(-3\) to \(-5\): \(-5 + (-3) = -8\), which matches the original statement showing -8 as the result. Therefore, our solution is correct.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Solving Linear Equations
Linear equations are equations where the highest power of the variable is one. These are the simplest types of equations and form the foundation for more complex algebraic thinking.
Solving linear equations involves finding the value of an unknown variable that makes the equation true. This process usually involves several steps:
Solving linear equations involves finding the value of an unknown variable that makes the equation true. This process usually involves several steps:
- Identify the unknown: First, identify the variable that you need to solve for. In our case, it's \( x \).
- Set up the equation: Most problems give a word description that you'll need to turn into an equation. For example, we have \( -5 + x = -8 \).
- Isolate the variable: Use inverse operations to solve for the variable. This is usually done by adding, subtracting, multiplying, or dividing both sides by a number.
- Verify the solution: Once you've found a solution, substitute it back into the original equation to ensure that both sides equal.
Prealgebra Concepts
Prealgebra is all about understanding basic mathematical operations and concepts that act as the building blocks for algebra. It involves working with numbers, understanding equations, and recognizing patterns.
Some important prealgebra concepts include:
Some important prealgebra concepts include:
- Understanding integers: Integers are whole numbers that can be positive, negative, or zero. Knowing how to work with them is essential because they often appear in algebraic equations.
- Basic operations: Operations such as addition, subtraction, multiplication, and division are fundamental. Mastering these operations is crucial as they are frequently used when simplifying and solving equations.
- Constructing and solving simple equations: Prealgebra sets the stage for understanding how to construct and solve simple equations, like the one given in our exercise: \( -5 + x = -8 \).
Integer Operations
Integer operations refer to the arithmetic operations that involve integers: addition, subtraction, multiplication, and division. In the context of solving linear equations, understanding how to perform these operations correctly is crucial.
For instance, in the exercise, you had to add integers, a common operation:
For instance, in the exercise, you had to add integers, a common operation:
- Addition of integers: When adding integers with the same sign, add their absolute values and give the result the same sign. For numbers with different signs, subtract the smaller absolute value from the larger one, and give the result the sign of the number with the larger absolute value.
- Subtraction of integers: Subtraction can be thought of as adding the opposite. To subtract an integer, add its opposite. This concept was useful when isolating \( x \) in the equation \( -5 + x = -8 \).
