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The process of isolating a variable is crucial when solving linear equations. This method allows us to express the variable of interest on one side of the equation, while everything else is moved to the opposite side. By doing so, we can easily identify the value of the unknown variable.In the equation \( y - 1.2 = -1.3 \), the goal is to isolate \( y \). We achieve this by performing inverse operations. Here, "\(-1.2\)" is subtracted from \( y \). To counteract this, we add \( 1.2 \) to both sides of the equation. This step ensures that we maintain the equality:

• Adding \( 1.2 \) results in: \( y - 1.2 + 1.2 = -1.3 + 1.2 \)
• The equation simplifies to \( y = -0.1 \)

This process demonstrates how essential it is to use inverse operations to successfully isolate and solve for variables.

Once a potential solution is found, it’s important to verify its correctness by substituting it back into the original equation. This step ensures that the solution not only satisfies the modified equation but also its initial terms.Continuing with our example, we found \( y = -0.1 \) as a solution. To verify this, substitute \( y = -0.1 \) back into the original equation \( y - 1.2 = -1.3 \):

• Substitute: \(-0.1 - 1.2 = -1.3\)
• Calculate the left-hand side: \(-0.1 - 1.2 = -1.3\)

Since both sides of the equation match, we confirm that \( y = -0.1 \) is the correct solution. Always remember to verify your solution to avoid mistakes and ensure your answer is reliable.

Understanding algebraic expressions is an essential skill when working with linear equations. An algebraic expression includes variables, numbers, and operation symbols.In our problem scenario, the expression \( y - 1.2 = -1.3 \) serves as a linear equation:

• "\( y \)" is our variable
• "\(-1.2\)" and "\(-1.3\)" are constants
• The operation between \( y \) and \(-1.2\) is subtraction

To manipulate these expressions, we use algebraic rules and operations such as addition, subtraction, multiplication, and division. Simplifying and rearranging expressions is integral to solving equations, making the understanding of these expressions vital. It's the foundation upon which solving techniques are built.