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Chapter 9: Problem 340

In the following exercises, solve. Solve a + b = 90 for a.

Short Answer

Expert verified
a = 90 - b

Step by step solution

01

Identify the equation

The given equation is: a + b = 90
02

Isolate variable a

To isolate the variable a, subtract b from both sides of the equation: a + b - b = 90 - b
03

Simplify the equation

By subtracting b from both sides, we get: a = 90 - b

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Key Concepts

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

Linear Equations
Linear equations form the backbone of many algebra problems. These equations typically involve variables raised to the power of one, making them 'linear'. In the exercise, we encountered the equation: \[a + b = 90\]. Linear equations usually have the following characteristics:
  • They represent straight lines when graphed.
  • They contain no exponents higher than one.
  • They can have one, none, or infinitely many solutions.
Understanding these basics helps navigate more complex algebraic expressions. Linear equations often require us to solve for one variable in terms of another, as we did by isolating \(a\) in \(a + b = 90\). This groundwork helps us build up to more sophisticated algebra problems.
Variable Isolation
Variable isolation is crucial in solving equations. Our goal in this exercise was to solve for \(a\). This involves isolating \(a\) on one side of the equation. Here, we started with:
  • \(a + b = 90\)
  • To isolate \(a\), we needed to perform the same operation on both sides of the equation.
In this example, we subtracted \(b\) from both sides: 馃敆\[a + b - b = 90 - b\]
This gets us: \[a = 90 - b\]
By isolating the variable, we solved the equation clearly. Remember, whatever you do to one side of the equation, you must do to the other to keep the equation balanced. This technique is foundational in algebra.
Basic Algebra
Basic algebra revolves around understanding symbols and their interactions. In our exercise, we used simple operations like addition and subtraction within the equation \(a + b = 90\). Understanding the fundamental operations and properties of numbers is essential:
  • Addition: Combining two quantities.
  • Subtraction: Removing a quantity from another.
Basic algebra frequently involves these operations to manipulate and solve equations. Here, we subtracted \(b\) to isolate \(a\), demonstrating how basic arithmetic skills integrate into algebra. Practicing these core skills strengthens your overall math abilities, making more convoluted problems easier to tackle.

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