91Ó°ÊÓ

The substitution method is a straightforward technique. It helps us solve equations and inequalities by replacing a variable with a given value. Let's dive into this method:
First, identify the variable and value to substitute. From our exercise, the inequality is \(4 - x \geq 3\), and we are given \(x = 1\). Substitution simply involves plugging the value into the variable:
- Replace \(x\) with \(1\)
- Our inequality now looks like this: \(4 - 1 \geq 3\).
By performing the substitution, we've prepared the inequality so that we can easily check if the resulting statement is true or false. Substitution is a handy tool, not just for solving inequalities, but also when dealing with equations and complex expressions.

Simplifying expressions is the process of making mathematical expressions easier to work with. In our exercise, we simplify after performing the substitution.
We replaced \(x = 1\) in \(4 - x \geq 3\), transforming it into \(4 - 1 \geq 3\).
Next, we simplify the left-hand side of the inequality, \(4 - 1 = 3\).
After simplification, our inequality reads \(3 \geq 3\). Simplifying helps us deal with more manageable numbers and operations, making it easier to understand whether the inequality holds. Always remember that the goal is to reduce the expression to its most basic form without changing its value or meaning.

Verifying solutions ensures that our substitutions and simplifications are correct and that the inequality holds true. After simplifying to \(3 \geq 3\), we must check if this statement is valid.
In our example, \(3 \geq 3\) is true because three is indeed equal to three. Verification means confirming that the mathematical statement we end up with accurately reflects the original problem's criteria.
Here are the steps to verify solutions effectively:
- Substitute and simplify the expression.
- Compare both sides of the inequality.
- Confirm if the simplified inequality is a valid statement.
By verifying, we gain confidence that our calculations are correct and that the given value meets the required conditions of the inequality.