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Understanding the distributive property is crucial when solving inequalities. This property allows us to remove parentheses by distributing a factor across each term within the parentheses. For example, if we have the expression \( 2(2x+3) \), we apply the distributive property by multiplying 2 with both \( 2x \) and 3, to get \( 4x + 6 \).

The distributive property isn't just about numbers; it applies to variables too. When you encounter inequalities like \(2(2x+3)-10 < 6(x-2)\), it's important to distribute correctly. On the left side, we multiply 2 by \(2x\) and 3, which results in \(4x + 6 - 10\). On the right side, we multiply 6 by \(x\) and -2, giving us \(6x - 12\). This step sets the stage for combining like terms and moving towards isolating the variable, a process critical for finding the inequality's solution.

To 'isolate the variable' means to get the variable on one side of the inequality, while everything else moves to the opposite side. This step is key in solving inequalities and equations alike, as it helps to find the value range of the variable.

In our example, to isolate \(x\), we aim to cancel terms involving \(x\) on one side. We subtract \(4x\) from both sides, transforming the inequality into \(4x - 4 - 4x + 12 < 6x - 12 - 4x + 12\), which simplifies to \(8 < 2x\). Adding or subtracting the same amount on both sides of an inequality does not change its direction. Hence, the inequality remains consistent even after these operations, bringing us closer to revealing the solution for the variable \(x\).

The final step in solving inequalities is to determine the exact solution or range of solutions for the variable. Once the variable is isolated, as in our simplified expression \(8 < 2x\), the next move is typically to divide or multiply both sides of the inequality by a positive number to solve for \(x\).

In this instance, we divide by 2 on both sides to get \(4 < x\), which is the same as saying \(x > 4\). It's important to note that multiplying or dividing both sides of an inequality by a negative number requires us to flip the inequality sign to maintain the true relation between the sides. However, since we divided by a positive number, the direction of the inequality doesn't change. Thus, the solution indicates that the values of \(x\) greater than 4 satisfy the original inequality. Understanding how to verify and graph these solutions can further assist in grasping the concept.