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Solving equations is a foundational skill in algebra that enables students to find the value of unknown variables. An equation is like a scale that must remain balanced. To solve an equation, we perform operations such as addition, subtraction, multiplication, or division to both sides, aiming to isolate the variable.

For example, in the given exercise, we have an equation where three times a number, represented by 'x', is divided by 6, equaling 10.5. The solution involves performing operations that reverse the equation's initial operations. In this case, we multiply both sides by 6 to cancel out the division and then divide by 3 to isolate 'x'. These steps maintain the balance of the equation and reveal that the unknown number 'x' is 21.

Linear equations are algebraic expressions that represent a straight line when graphed on a coordinate plane. They have one or more variables but do not contain variables raised to a power higher than one or variables multiplying each other.

A simple example of a linear equation is the form 'ax + b = c', where 'a', 'b', and 'c' are constants. The solution in our exercise is an example of a linear equation, where we started with an equation in the form of \(\frac{{3x}}{6} = 10.5\) and solved it to find 'x'. Linear equations are crucial because they model many real-world phenomena, like calculating distances, costs, and other quantities.

Mathematical expressions are combinations of numbers, variables, and operation symbols that represent a specific value or set of values. Unlike equations, expressions do not have an 'equals' sign. They form the building blocks of equations and can be simplified or manipulated according to the rules of algebra.

In the context of our exercise, \(3 * x / 6\) is a mathematical expression that we simplify as part of solving the equation. Understanding how to work with expressions, such as combining like terms and using the distributive property, is critical to solving more complex algebra problems.