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Chapter 2: Problem 1

For exercises 1-10, solve. $$ x+8=24 $$

Short Answer

Expert verified
x = 16

Step by step solution

01

Understand the Equation

The equation given is a simple linear equation: $$x + 8 = 24$$. The goal is to find the value of the variable (\
02

Isolate the Variable

To isolate the variable on one side of the equation, subtract 8 from both sides of the equation: $$x + 8 - 8 = 24 - 8$$.
03

Simplify Both Sides

Simplify the equation after performing the subtraction: $$x = 16.$$.

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Key Concepts

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

Isolate the Variable
In algebra, 'isolating the variable' means to get the variable alone on one side of the equation. This is important because it allows you to determine the value of the variable.
In the equation given, $$x + 8 = 24$$, we need to isolate 'x'.
To do this, we perform the same operation on both sides of the equation. This keeps the equation balanced.
Subtract 8 from both sides to get:x + 8 - 8 = 24 - 8, which simplifies to $$x = 16$$.
Remember, always perform the same operation on both sides when isolating the variable.
Simplify the Equation
Simplifying an equation means to make it less complex. This involves combining like terms and performing operations to make the expression easier to work with.
In the exercise, once we subtract 8 from both sides, we simplify each side. $$24 - 8$$ simplifies to 16, and $$x + 8 - 8$$ simplifies to just $$x$$, because the +8 and -8 cancel each other out.
Simplification leaves us with: $$x = 16$$.
This simplified form tells us the value of $$x$$ in a clear and concise way. Always aim for the simplest form when solving equations.
Basic Algebra
Basic algebra involves working with variables, constants, and arithmetic operations to solve equations. It's essential to understand these core principles:
- An equation represents a balance, meaning both sides are equal.
- Operations performed on one side must be performed on the other to maintain balance.
- Always aim to combine like terms and reduce the equation to its simplest form.
In the given exercise, we started with the equation: $$x + 8 = 24$$. Using basic algebra principles, we isolated the variable and simplified both sides to find: $$x = 16$$.
Understanding these fundamental steps will help in solving more complex algebraic equations in the future.

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