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Basic algebra is foundational to understanding and solving equations. It involves using simple operations such as addition, subtraction, multiplication, and division to manipulate an equation and find the value of unknowns, often represented by variables like \(x\). In this exercise, we start with the equation \(x + 10 = 17\). Basic algebra teaches us to understand each part of this equation:

• The variable \(x\) represents an unknown that we need to find.
• The number \(10\) is added to \(x\) and is known as a constant.
• The equation is set to equal \(17\), the result of the left side.

Knowing these components helps guide our steps to solving the equation.

Equation solving is the process of finding the value of the unknowns in an equation. It requires systematically applying mathematical operations to balance and simplify both sides of the equation.For the equation \(x + 10 = 17\), we want to make sure that both sides remain equal as we perform operations. ### Step-by-Step Process- Begin by examining the structure of the equation. Recognize that our goal is to find the value of \(x\).- Utilize inverse operations to counteract addition or subtraction, ensuring equal changes on both sides of the equation.In this example, we need to remove the \(+10\) from the left side to isolate \(x\). By subtracting \(10\) from both sides, we maintain balance while simplifying the equation. This method of solving is key to unraveling the value of \(x\).

Variable isolation is a crucial technique in solving equations. The idea is to "isolate" the variable on one side of the equation, transforming the equation so that it reads as \(x = \text{something}\).Here’s how it works in the equation \(x + 10 = 17\):- **Step 1:** Target the variable \(x\). To do this, any constant term (like \(10\) in this case) must be moved to the other side of the equation.- **Step 2:** Perform inverse operations. Since \(x\) is being added to \(10\), you subtract \(10\) from both sides: \(x + 10 - 10 = 17 - 10\).- **Step 3:** Simplify both sides. After subtraction, you're left with \(x = 7\). This completes the isolation, revealing that \(x\) equals \(7\).By following these simple steps, you can solve and isolate variables in basic algebraic equations effectively.