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Chapter 2: Problem 21

Solve using the addition principle. Don't forget to check! $$ y+7=-4 $$

Short Answer

Expert verified
y = -11

Step by step solution

01

Identify the Equation

The given equation is: \[ y + 7 = -4 \]
02

Apply the Addition Principle

To isolate the variable \( y \), subtract 7 from both sides of the equation: \[ y + 7 - 7 = -4 - 7 \]
03

Simplify Both Sides

Simplify the equation to find \( y \): \[ y = -11 \]
04

Check the Solution

Substitute \( y = -11 \) back into the original equation to verify it is correct: \[ -11 + 7 = -4 \] \[ -4 = -4 \] Since both sides of the equation are equal, the 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
Solving linear equations involves finding the value of the unknown variable that makes the equation true. Linear equations are generally straightforward to solve. Here, we'll tackle an essential problem using the addition principle. The equation given is: \[ y + 7 = -4 \] This is a simple linear equation with one variable, \(y\). Our goal is to determine the value of \(y\) that satisfies the equation. We can achieve this by isolating the variable, ensuring that \(y\) is on one side of the equation, and the constants are on the other side.
isolate the variable
Isolating the variable means getting the unknown variable on one side of the equation, usually by itself. In this problem, \(y\) is our variable: \[ y + 7 = -4 \] To isolate \(y\), we need to eliminate the 7 added to it. This is where the addition principle comes in handy. We subtract 7 from both sides of the equation to keep it balanced: \[ y + 7 - 7 = -4 - 7 \] Simplifying both sides, we get: \[ y = -11 \] Now, we have isolated \(y\) and found that \(y = -11\). This technique is applicable to all linear equations where we need to isolate the variable.
checking solutions
After solving the equation, it is important to verify that your solution is correct. We do this by substituting the found value back into the original equation. Our equation was: \[ y + 7 = -4 \] With \(y\) found to be \(-11\), let's substitute it back in: \[ -11 + 7 = -4 \] Simplifying the left side, we get: \[ -4 = -4 \] Since both sides of the equation are equal, our solution is verified to be correct. This step confirms that \(y = -11\) is indeed the correct solution. Always remember to check your solutions to ensure accuracy.

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