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Chapter 5: Problem 295

In the following exercises, solve the equation. $$ c+1.15=-3.5 $$

Short Answer

Expert verified
c = -4.65

Step by step solution

01

- Isolate the variable

To solve for the variable \(c\), begin by isolating \(c\). To do this, subtract 1.15 from both sides of the equation.
02

- Perform the subtraction

Subtract 1.15 from \(-3.5\). \(-3.5 - 1.15 = -4.65\). Now the equation simplifies to: \(c = -4.65\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the Variable
When solving linear equations, the first step is to isolate the variable. The goal is to get the variable alone on one side of the equation.
In the given exercise, our variable is `c`. The initial equation is:
\(c + 1.15 = -3.5\).
To isolate `c`, we need to remove the 1.15 that is added to it.
We can do this by performing an inverse operation, which leads us to the next step - subtraction.
Subtraction
Subtraction is an essential operation in algebra, especially for isolating variables. Here, we need to subtract 1.15 from both sides to keep the equation balanced.
This action is based on the principle of maintaining equality.
When we subtract 1.15 from both sides of our equation, it looks like this:
\(c + 1.15 - 1.15 = -3.5 - 1.15\).
On the left side, the 1.15 cancels out, leaving us with just `c`:
\(c = -4.65\).
This step is crucial for isolating the variable and solving the equation.
Negative Numbers
Understanding negative numbers is key when solving linear equations.
When we subtract a positive number from a negative number, the result is further negative.
In our example, after subtracting 1.15 from -3.5, we get:
\(-3.5 - 1.15 = -4.65\).
Think of it as moving leftwards on a number line; you start at -3.5 and move 1.15 units further to the left. This gives us -4.65.
Being comfortable with negative numbers will help in successfully solving equations like this one.

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