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Linear equations are mathematical statements where each term is either a constant or the product of a constant and a single variable. In simpler terms, it's an equation that forms a straight line when graphed. The general form of a linear equation in one variable is often expressed as: \[ax + b = c\] Here, 'a', 'b', and 'c' are constants, and 'x' is the variable. To solve a linear equation, we follow steps to simplify the equation and isolate the variable. Let's review our example \[2(x + 5) = 14\]. We begin by recognizing that this is a linear equation because the variable 'x' is raised to the power of 1, implying a linear relation. Key characteristics of linear equations include:

• They graph as straight lines.
• They have one solution when involving one variable.
• They often involve operations like addition, subtraction, multiplication, and division to solve.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. It's about finding the unknown or putting real-life variables into equations and then solving them. In our example, to solve the linear equation \[2(x + 5) = 14\],we need some fundamental algebraic skills:

• **Expanding the equation**: Use the distributive property to multiply 2 into \(x + 5\). This results in \(2x + 10 = 14\).
• **Simplifying equations:** Combine like terms and simplify the equation wherever possible.
• **Manipulating equations:** Use inverse operations to isolate the variable. For instance, subtract 10 from both sides to focus on the term involving x.

These algebraic methods are crucial as they allow us to rearrange and manipulate equations to find solutions effectively.

Isolating the variable means rearranging the equation so that the unknown variable (x, in our case) stands alone on one side of the equation. This process is essential because it allows us to find the specific value of the variable. For instance, let's revisit our equation \(2x + 10 = 14\).

• **Step 1**: Subtract 10 from both sides. This gives us \(2x = 4\).
• **Step 2**: Divide both sides by 2. This isolates 'x' and we get \(x = 2\).

By performing these operations, we effectively isolated 'x', solving the equation in a systematic and clear manner. Remember, isolating the variable often requires using inverse operations such as:

• Adding or subtracting the same number from both sides.
• Multiplying or dividing both sides by the same non-zero number.