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Chapter 3: Problem 4

Solve the equation mentally. $$a+5=0$$

Short Answer

Expert verified
The solution to the equation \(a+5=0\) is \(a = -5\).

Step by step solution

01

Understand the equation

The equation presented is a linear equation and has the form \(a + 5 = 0\). The goal is to find the value of \(a\) that makes the equation true.
02

Rearrange the equation

The next step is to isolate \(a\), this can be achieved by performing the same operation on both sides of an equation to maintain equality. In this case, subtract 5 from both sides: \(a + 5 - 5 = 0 - 5\).
03

Calculate 'a'

Solve \(a = 0 - 5\), getting \(a = -5\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mastering Mental Math
When solving linear equations like \(a + 5 = 0\), you might be tempted to use paper and pencil or a calculator. However, mental math can simplify the process significantly. By improving your mental math skills, you learn to quickly identify the steps.Mental math involves intuition in recognizing patterns. It enables us to spot relationships between numbers. For this equation, recognize the number that combines with 5 to make zero.
  • Think of it as a simple subtraction problem: "What added to five equals zero?"
  • Quickly, notice that \(-5\) added to 5 gives zero.
Mental math is not just about calculation but pattern recognition. With practice, you'll solve more complex equations easily, relying less on paper.
Understanding Algebraic Manipulation
Algebraic manipulation is a core skill in solving equations effectively. It involves rearranging equations to isolate the variable. This skill lets you transform any equation into a simpler form, allowing easier solutions. Understanding operations that affect the equation is crucial.In our example, \(a + 5 = 0\), subtract 5 from both sides. Why? Because the goal is to isolate \(a\) on one side.
  • Identify the operation on the variable: Here, it's addition.
  • Use the inverse operation to cancel it out: subtract 5.
  • This leaves you with \(a = 0 - 5\).
Algebraic manipulation isn't limited to addition or subtraction. Learn to apply these skills to multiplication, division, and other operations.
Solving Linear Equations
Equation solving is like piecing together a puzzle where each step brings you closer to the solution. For linear equations such as \(a + 5 = 0\), follow a structured approach to find the answer.The basic principle is to isolate the variable. This involves performing opposite operations while maintaining balance in the equation.
  • Identify the operation binding the variable: For \(a + 5\), it's addition.
  • Apply the inverse: Subtraction, so subtract 5 from both sides.
  • Find the solution: Solve \(a = -5\).
Each step in the process is essential. Carefully using these methods ensures you obtain the correct solution. Practice different problems to become proficient.

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Most popular questions from this chapter

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