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Solving inequalities is akin to solving equations, but with a few additional rules. When we solve an inequality, we are finding a range of values that satisfy the given condition.

In this exercise, the initial condition is given as: \(x < 5\). By using algebraic manipulation, we subtract 5 from both sides of the inequality to eventually isolate the term of interest. This process is similar to solving an equation but with extra care to maintain the inequality's direction. Remember, the direction of the inequality matters and reflects the relationship between the left and right sides.

A vital rule to note is: Whenever both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality reverses.

Inequality symbols are used to compare two values. Understanding these symbols is crucial for solving inequalities correctly.

Here are the key inequality symbols:

• < : less than
• > : greater than
• ≤ : less than or equal to
• ≥ : greater than or equal to

In our exercise, the inequality symbol '<' tells us that the value of \(x\) should be less than 5. Knowing these symbols helps in visualizing the inequality and in representing it on a number line efficiently. While solving inequalities, always ensure the correct symbol is used to represent the relationship accurately.

Algebraic manipulation involves changing the form of an equation or inequality to make it simpler to solve. This often includes addition, subtraction, multiplication, and division.

Here’s how we use algebraic manipulation in the provided exercise:

• Step 1: Start with the given inequality \(x < 5\).
• Step 2: Subtract 5 from both sides to maintain the balance of the inequality: \(x - 5 < 5 - 5\).
• Step 3: Simplify the expression: \(x - 5 < 0\).

Now, we have the final simplified inequality. Manipulating inequalities follows similar rules as manipulating equations, with special attention to maintaining direction and understanding the symbols' meaning. Practicing these steps ensures mastery in solving various inequality problems.