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Inequality solving is a fundamental aspect of algebra that involves finding the values of variables that satisfy a given inequality relationship. An inequality, unlike an equation, indicates that one side is not necessarily equal to the other, but rather greater than, less than, or possibly equal to, within a range of values.

When solving an inequality, such as the given exercise where we have to solve for x in the inequality 7x > 2, the first objective is to isolate the variable. This is done by performing the same mathematical operations on both sides of the inequality, ensuring the relationship between the sides remains consistent.

A crucial aspect to remember during inequality solving is the rule about reversing the inequality symbol when multiplying or dividing by a negative number. However, in our example, since we divide by a positive 7, the direction of inequality remains the same, thus affirming x is greater than 2/7. The resulting intervals of values that solve our inequality will be an integral part in forming the correct interval notation.

Isolating variables is a strategy used in both equations and inequalities to solve for an unknown. The goal is to get the variable on one side of the inequality (or equation) by itself to determine its value within the context of the problem. When isolating variables, you can add, subtract, multiply, or divide both sides by the same non-zero number.

In our example, the variable x is initially part of the term 7x. To isolate x, we divided both sides of the inequality by 7. It's important to perform the operation on both sides to maintain the balance of the inequality. After dividing, we obtain x > 2/7.

It's imperative for learners to grasp that isolating the variable is a critical step to solving inequalities as well as equations. The same rules apply: whatever operation you do to one side, you must do to the other, and always be cognizant about the direction of the inequality when dealing with negative coefficients.

Open intervals are a way to describe a range of numbers that includes all the numbers between two endpoints, but not the endpoints themselves. In interval notation, open intervals are represented by parentheses '()' as opposed to brackets '[]', which would indicate a closed interval where the endpoints are included.

The solution to the inequality x > 2/7, in interval form, is expressed as \(\frac{2}{7} , +\infty)\). The parenthesis around 2/7 implies that this value is not part of the solution set. The plus infinity symbol (\(+∞\)) indicates that there is no upper bound to the values x can take; it can grow infinitely large and still satisfy the inequality.

Understanding open intervals is crucial when dealing with continuous variables. It's worth noting that mathematical expressions are carefully designed to indicate the precise nature of ranges - with open intervals representing just one type of interval notation that students will encounter.