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When solving inequalities, it's crucial to first isolate the variable. This means rearranging the equation so that the variable (\(x\) in our example) stands alone on one side of the inequality sign. Let's break down why this is necessary:

• Isolating the variable helps us focus on finding the value of the variable that makes the inequality true.
• It involves reversing mathematical operations that are affecting the variable. For instance, in the inequality \(3x + 2 > 17\), we have an addition operation that needs to be undone.

We'll start by eliminating any constants from the side of the inequality where the variable is. In our example, this means subtracting 2 from both sides, resulting in \(3x > 15\). Notice how this step simplifies the inequality and moves us closer to discovering the solution.

Understanding the properties of inequalities is fundamental when solving them. Here are some key principles to keep in mind:

• Whatever operation you apply to one side of the inequality, you must apply to the other side as well. This maintains the balance of the inequality.
• If you multiply or divide both sides of an inequality by a positive number, the direction of the inequality sign remains unchanged. If you multiply or divide by a negative number, the direction of the inequality sign flips.

In the example \(3x > 15\), we divide both sides by 3 (a positive number) to solve for \(x\). This keeps the inequality direction intact, resulting in \(x > 5\). This demonstrates how steps need to be taken cautiously to ensure the inequality's integrity is preserved, especially when dealing with negative numbers.

Approaching inequalities in a methodical, step-by-step manner ensures accuracy and clarity. Let's review the steps applied in our given problem:**Step 1: Subtract the Constant** We identified a constant in the inequality \(3x + 2 > 17\). By subtracting 2 from both sides, we clarify the inequality to \(3x > 15\).**Step 2: Divide by the Coefficient** With the inequality \(3x > 15\), the variable \(x\) is multiplied by 3. To isolate \(x\), divide both sides by 3. This yields the solution \(x > 5\).Following these steps helps you solve the inequality efficiently. Each operation moves you closer to understanding the range of possible values for the variable. The solution \(x > 5\) tells us that any number greater than 5 will satisfy the initial inequality \(3x + 2 > 17\).