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When we talk about solving equations, we mean finding the value of the variable that makes the equation true. In our example, the equation is \(2x + 3 = 7\). Solving it means finding the value of \(x\) that, when substituted into the equation, satisfies both sides. Solving equations involves manipulating the equation to isolate the variable while keeping the equation balanced. Each operation we perform on one side of the equation has to be done on the other side as well. This maintains the equality and helps us narrow down the possible values for the variable. Equations can range from simple, like the one here, to more complex ones that may require multiple steps including operations like addition, subtraction, multiplication, or division. However, the main goal remains the same: isolate the variable and solve for it.

Isolation of variables is a crucial step in solving equations. Essentially, it means getting the variable by itself on one side of the equation so you can see what it equals. In the given problem, we start with \(2x + 3 = 7\). The first step is to move the constant term, which is 3, away from the variable. This is done by subtracting 3 from both sides leading to \(2x = 4\). Here are some key points about variable isolation:

• Deal with addition or subtraction first, to simplify the equation.
• Use inverse operations to "undo" what is being applied to the variable.
• Keep the equation balanced by performing the operation on both sides.

Once you simplify as much as possible, you are usually left with the variable multiplied or divided by a number. Divide or multiply accordingly to finish the isolation, just as we divided by 2 to solve for \(x\). This resulted in \(x = 2\).

Algebra involves using symbols, usually letters, to represent numbers in equations or formulas. It helps in finding unknown values. Basic algebra often begins with understanding variables, equations, and functions. In our exercise, the variable is \(x\), an unknown we need to find. Equations like \(2x + 3 = 7\) show the relationship of numbers and variables. Some basic algebra concepts include:

• Variables: Symbols that stand in for unknown values.
• Constants: Known values in equations (like 3 in our example).
• Operations: Basic math operations such as addition, subtraction, multiplication, or division used to solve equations.

These concepts allow us to restructure problems and solve them systematically. Step-by-step problem solving is encouraged, emphasizing the manipulation each step follows logically from the previous one, ensuring accuracy and understanding.