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Chapter 11: Problem 21

Solve using the addition principle. $$ y-8=-9 $$

Short Answer

Expert verified
y = -1

Step by step solution

01

Identify the equation

The equation given is t y-8=-9.
02

Add 8 to both sides

To isolate the variable y on one side of the equation, add 8 to both sides of the equation: n y - 8 + 8 = -9 + 8.
03

Simplify both sides

Simplify both sides of the equation to solve for the variable y: y = -1.

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Key Concepts

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

solving equations
Solving equations means finding a value for the variable that makes the equation true. In our exercise, the equation is given as \(y - 8 = -9\). The goal is to isolate the variable \(y\) on one side of the equation. By adding 8 to both sides, we use one of the fundamental principles of equation solving鈥攖he addition principle. This principle helps maintain the balance of the equation because whatever you do to one side, you must do to the other. This way, we find that \(y = -1\), which is the solution to the equation.
basic algebra
Basic algebra involves understanding simple operations and their applications to solve equations. In our example, the given equation is \(y - 8 = -9\). Let's break this down:
  • We start with subtraction: 8 is subtracted from \(y\).
  • To counteract this, we add 8 to both sides.
  • This gives us: \(y - 8 + 8 = -9 + 8\).
  • We then simplify both sides: \(y = -1\).

Algebra often deals with operations like addition, subtraction, multiplication, and division. Understanding these operations is crucial. This helps students comprehend more complex equations as they progress in mathematics.
isolation of variables
Isolating variables means getting the variable alone on one side of the equation, which makes it easier to solve for that variable. In our exercise, we start with \(y - 8 = -9\).
  • Our goal is to isolate \(y\), meaning we want \(y\) by itself on one side.
  • By adding 8 to both sides (\[y - 8 + 8 = -9 + 8\]), we cancel out the \(-8\) next to \(y\).
  • This simplifies to \(y = -1\), successfully isolating \(y\).

The key to the isolation of variables is performing inverse operations. Whether you're dealing with addition, subtraction, multiplication, or division, doing the opposite operation helps you isolate the variable.

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