91Ó°ÊÓ

When solving linear equations, the primary goal is to isolate the variable. In the given problem, we're working with the equation: \( c + 2 = -5 \). Isolating the variable means arranging the equation so that \( c \) stands alone on one side of the equation, free from other numbers or operations. To achieve this, we perform the inverse operation of what's currently being done to \( c \). Here, the number 2 is being added to \( c \). The inverse of addition is subtraction, so we subtract 2 from both sides of the equation:

• Subtract 2 from the left side: \( c + 2 - 2 = c \)
• Subtract 2 from the right side: \( -5 - 2 = -7 \)

The equation then simplifies to \( c = -7 \). By performing the same operation on both sides, we maintain the equality and successfully isolate \( c \). This allows us to see what value \( c \) must be to make the equation true.

After determining a potential solution to an equation, it is important to check that the solution actually works by plugging it back into the original equation. In this problem, after finding \( c = -7 \), we substitute \( -7 \) back into the original equation:\( c + 2 = -5 \).Replace \( c \) with \( -7 \) and simplify:

• Set up the equation with the solution: \( -7 + 2 \).
• Simplify the left side: \( -7 + 2 = -5 \).

By checking, you confirm that the solved equation holds true, because \( -5 \) equals \( -5 \). This is a crucial step in verifying your solution. If both sides of the equation don't match, you'd know there was an error that needs correcting.

Simple subtraction equations involve moving from a basic equation toward isolating a single variable through the process of subtraction. In the original exercise, \( c + 2 = -5 \), we simply had to subtract 2 to isolate \( c \).This type of problem is straightforward because it only involves one operation: subtraction. Here's a brief rundown of steps when solving such equations:

• Identify what number to subtract (here it's 2).
• Perform subtraction on both sides of the equation to maintain balance.
• Confirm the variable is isolated (\( c = -7 \) here).

Such problems typically require understanding the relationship between the numbers and the variable, maintaining balance in the equation through each step. By mastering simple subtraction equations, we build a strong foundation for tackling more complex algebraic equations later.