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Algebraic expressions involve combining numbers and variables using operations like addition, subtraction, multiplication, and division. In this exercise, the expression is given as \(7x - 9\), which includes both a variable term and a constant term. Understanding how to manipulate these expressions is crucial to solving algebraic equations and inequalities. By applying basic arithmetic operations, we aim to simplify such expressions to a form where the solution can be easily identified. When you want to isolate a variable, like \(x\), working with algebraic expressions means rearranging the terms according to mathematical rules. This usually involves moving terms across the inequality sign and performing operations to simplify the expression. Remember, what you do to one side of the inequality, you must do to the other. This is the key principle of maintaining balance in algebraic expressions and inequalities.

Graphing inequalities on a number line offers a visual representation of solutions. The inequality \(x > 2\) means that \(x\) includes all numbers greater than 2. To graph this, place an open circle at 2 on the number line because 2 is not included in the solution set. This shows that the solution set starts just after 2. Draw a line or arrow extending to the right from the open circle to represent that any number greater than 2 satisfies the inequality.

• Open circles indicate that the number is not included (\(<\) or \(>\)).
• Closed circles indicate that the number is included (\(\leq\) or \(\geq\)).
• An arrow shows the direction in which the inequality is true.

Graphing inequalities helps you see the range of possible solutions and provides a clear, visual understanding for better interpretation.

Isolation of variables is the process of manipulating an equation or inequality such that the target variable is alone on one side of the equality or inequality sign. Here, \(7x - 9 > 5\) needed transformation to isolate \(x\). The first move is to shift constants to the opposite side of the inequality, modifying it into \(7x > 14\).

The goal is to make the coefficient of \(x\) equal to 1, done by dividing both sides by 7, leading to \(x > 2\).

• Always perform the same operation on both sides of the equation or inequality.
• When multiplying or dividing by a negative number, remember to flip the inequality sign.
• Check your work by substituting values back to ensure accuracy.

Isolation is fundamental for solving inequalities, as it progresses the solution towards finding feasible values of \(x\). Understanding this concept allows students to solve more complex algebraic problems systematically and confidently.