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In algebra, evaluating expressions is the process of finding the numerical value of an expression. The expression often contains numbers, variables, and arithmetic operators. In our original exercise, we are given the expression \(|10-7|-|7-10|\).

To evaluate this, we need to perform the calculations inside each absolute value sign first. This means calculating the difference between the pairs of numbers.

Here’s how:

• Evaluate \(10 - 7\): This equals 3.
• Evaluate \(7 - 10\): This equals -3.

By breaking each part down step by step, it becomes easier to understand and solve the overall expression. Evaluation is a critical first step in solving more complex algebraic problems.

Simplifying expressions involves reducing them to their simplest form. This might include performing arithmetic operations or combining like terms. In our original problem, after evaluating the expressions inside the absolute value symbols, we simplify them further by dealing with the absolute values.

The absolute value of a number is its distance from zero on the number line, regardless of direction. Thus:

• \(|3| = 3\)
• \(|-3| = 3\)

Now, the expression becomes \((3 - 3)\).

It is important to note that the absolute value function turns all negative inputs into their positive equivalents. This simplifies the expressions and is key to solving them accurately. Without this step, we wouldn’t reach the correct solution.

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations are foundational in algebra and are used to simplify and solve expressions. In the exercise, subtraction is the primary operation:

\(3 - 3 = 0\).

Remember to always follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Applying these basic operations correctly is essential for obtaining the right answers in any algebraic problem. Practice makes perfect, so keep working through examples to build your skills!