Find the values of the variables for which each statement is true, if possible.

Verified step by step guidance

1. First, carefully read the problem statement to identify the given equations or expressions involving the variables. Since the problem references Examples 1 and 2, review those examples to understand the type of equations or statements you need to solve.
2. Next, write down the equations or inequalities explicitly. For example, if the problem involves solving for variables in an equation like \(ax + b = c\), write it clearly in LaTeX format.
3. Then, isolate the variable you want to solve for by performing algebraic operations such as addition, subtraction, multiplication, division, or factoring. Remember to apply the same operation to both sides of the equation to maintain equality.
4. After isolating the variable, simplify the expression as much as possible. This might involve combining like terms, reducing fractions, or applying inverse operations.
5. Finally, check your solution by substituting the found value(s) back into the original equation(s) to verify that the statements are true. If the substitution holds true, the solution is valid; if not, reconsider the steps or determine if no solution exists.

Key Concepts

Solving Algebraic Equations

This involves finding the values of variables that make an equation true. Techniques include isolating the variable using inverse operations such as addition, subtraction, multiplication, division, and applying properties of equality.

Understanding Variables and Expressions

Variables represent unknown values in algebraic expressions or equations. Recognizing how to manipulate expressions involving variables is essential to simplify and solve equations accurately.

Checking Solutions

After finding potential solutions, substituting them back into the original equation verifies their validity. This step ensures that the solutions satisfy the given statements and helps identify extraneous or invalid answers.