91Ó°ÊÓ

Algebraic equations are statements that show the equality between two mathematical expressions. In this exercise, we dealt with the equation: \[ x + 9 = -26 \] To solve this equation, our goal is to find the value of the variable 'x' that makes the equation true. The solution involves understanding that whatever operations you perform on one side of the equation, you must also perform on the other side. This ensures the equality remains balanced on both sides.

Isolation of variables refers to the process of manipulating an equation to get the unknown variable by itself on one side of the equation. In our case, we needed to isolate 'x'. To start, we had: \[ x + 9 = -26 \] To isolate 'x', we performed the same mathematical operation on both sides of the equation. Here, we subtracted 9 from both sides: \[ x + 9 - 9 = -26 - 9 \] By simplifying this, we successfully isolated 'x': \[ x = -35 \] This process was crucial to solving for the unknown variable.

Negative numbers are numbers less than zero, represented with a minus (−) sign. Understanding how to work with them is vital in solving equations. In this problem, both the given number and the solution involved negative numbers. For example, adding a negative number is the same as subtracting its positive counterpart. Similarly, subtracting a negative number is equivalent to adding its positive counterpart. In our step-by-step process, we encountered: \[ -26 \text{ (a negative number)} \] and needed to subtract 9 from it. This required recognizing that: \[ -26 - 9 = -35 \] Working with negative numbers correctly was essential to reaching the correct answer in this exercise.