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Chapter 3: Problem 43

Solve the equation. $$q-4=-12$$

Short Answer

Expert verified
The solution is \( q = -8 \).

Step by step solution

01

Identify the equation

The given equation is: \( q - 4 = -12 \)
02

Isolate the variable

To isolate \( q \), add 4 to both sides of the equation: \( q - 4 + 4 = -12 + 4 \)
03

Simplify both sides

Simplify the equation on both sides: \[ q = -8 \]

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Key Concepts

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

Isolating the Variable
Isolating the variable is a crucial concept when solving linear equations. The variable is the unknown part of the equation that you want to solve for.
In our example, the equation is: \[ q - 4 = -12 \] Here, 'q' is the variable. To isolate 'q', we need to move any numbers or constants to the other side of the equation.
Think of this like cleaning your room鈥攅verything that doesn't belong has to be put away. In this case, the -4 doesn't belong with the 'q'.
Adding to Both Sides
To isolate the variable, we can use a simple but powerful principle: what we do to one side of the equation, we must do to the other!
Adding to both sides helps maintain the balance of the equation. In our example, to remove the -4 next to 'q', we add 4 to both sides: \[ q - 4 + 4 = -12 + 4 \] Why add 4? Because -4 and +4 cancel each other out, simplifying our work.
This is like balancing a scale鈥攊f you add some weight to one side, you must do the same to the other side to keep it even.
Simplifying Equations
The last step in solving our equation is to simplify both sides after adding: \[ q - 4 + 4 = -12 + 4 \] On the left side, -4 and +4 cancel out, leaving us with: \[ q = -8 \] Simplifying is like taking the final step to clean up your equation.
This step makes sure the equation is clear and the variable stands alone.
  • Check your answer: You can always plug your solution back into the original equation to verify.
In this case, substitute -8 for 'q' back into the equation: \[ -8 - 4 = -12 \] Since both sides are equal, you know your solution is correct!

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