91Ó°ÊÓ

When solving inequalities, the first step often involves combining like terms. **Like terms** are terms that contain the same variable raised to the same power. In this context, both \(-2x\) and \(2x\) are like terms because they contain the same variable \(x\) raised to the same power (which is 1, even though it's not explicitly written).By combining like terms, you simplify the expression to make it easier to work with. In our exercise, when we add \(-2x\) and \(2x\), they effectively "cancel each other out" because their sum is zero. This step is crucial because it reduces the complexity of the inequality, leaving us with just numbers or simpler expressions that are easier to interpret.Always remember to pay attention to the signs in front of each term as these dictate whether you add or subtract.

• Positive and negative terms with the same variables are combined by adding their coefficients.
• For \(-2x + 2x\), the result is \(0x\) or just \(0\).

Once like terms are combined, the next step in solving the inequality involves simplifying it further. Simplification might include removing extraneous terms or constants so that you can clearly see the relationship between the remaining numbers or expressions.In our exercise, after cancelling the \(-2x\) and \(2x\), we are left with just constants: \(7 > 1\). There's no variable left, just a straightforward numerical expression. Such an outcome makes the inequality easy to interpret as no further steps are needed to manipulate the inequality.Applying simplification helps us:

• Uncover the true nature of the inequality, determining whether it is valid throughout its domain.
• Identify possible outcomes concerning different values of the variable involved.

Simplifying inequalities is a foundational step in algebra that leads to efficient problem-solving and clearer results.

When solving inequalities, the end goal often is to arrive at a **true statement**. A true statement is essentially a numerical inequality or equation where the left and right sides agree with the mathematical relationships presented.In our simplified result, the inequality \(7 > 1\) obviously holds as a true statement. This tells us that the original inequality is satisfied regardless of the variable's value — this happens because all terms involving the variable were eliminated during simplification.True statements in inequalities confirm that:

• The inequality is valid.
• There are no restrictions or specific solutions for the variable since it cancels entirely in this context.

It indicates that any value for the variable holds power in satisfying the original inequality, which is particularly insightful in variable-rich expressions where understanding scope is key. This results in potentially broader solutions, or simply an affirmation of the inequality's inherent truth.