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Chapter 2: Problem 39

Solve using the addition principle. Don't forget to check! $$ -9.7=-4.7+y $$

Short Answer

Expert verified
The solution is \(y = -5\).

Step by step solution

01

Isolate the Variable

The given equation is \(-9.7=-4.7+y\). To isolate \(y\), use the addition principle. Add \(4.7\) to both sides of the equation to cancel out the \(-4.7\) on the right side.
02

Perform the Addition

Add \(4.7\) to both sides: \(-9.7 + 4.7 = -4.7 + 4.7 + y\). This simplifies to \(-5 = y\).
03

Rewrite the Equation

The simplified equation after adding \(4.7\) to both sides is \(-5 = y\).
04

Check the Solution

Substitute \(y = -5\) back into the original equation to verify: \(-9.7 = -4.7 + (-5)\). Simplify the right side: \(-9.7 = -9.7\). The original equation holds true, so \(y = -5\) is correct.

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Key Concepts

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

Solving Equations
When solving equations, the goal is to find the value of the variable that makes the equation true. In this exercise, we were given the equation \( -9.7 = -4.7 + y \). To make things easier, we need one side to be just the variable we are solving for, in our case, \( y \). Solving equations often involves several steps: identifying the operation being used, performing the reverse operation to both sides, and simplifying until the variable is isolated. Understanding these steps helps demystify the process and makes equations less intimidating.
Isolate the Variable
To isolate the variable means to get the variable alone on one side of the equation. In this case, we want to isolate \( y \). The given equation is \( -9.7 = -4.7 + y \).
Here's a step-by-step breakdown:
  • Add \( 4.7 \) to both sides of the equation. By doing this, we aim to cancel out the \( -4.7 \) on the right side. The new equation is: \( -9.7 + 4.7 = -4.7 + 4.7 + y \).

  • Simplify both sides. This gives us \( -5 = y \).

  • Our isolated variable is \
Verify Solution
Once we have isolated the variable and solved for it, we need to verify the solution. Verification ensures that the solution is correct and satisfies the original equation.
To verify \( y = -5 \):
  • Substitute \( -5 \) for \( y \): \( -9.7 = -4.7 + (-5) \).

  • Simplify the right side: \( -4.7 + (-5) = -9.7 \).

  • Both sides match, so our solution \( y = -5 \) is verified and correct.
Verifying solutions is essential as it confirms that all steps were done correctly and the found value indeed solves the original equation.

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Most popular questions from this chapter

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