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Chapter 3: Problem 60

Solve the equation. $$11=-q$$

Short Answer

Expert verified
q = -11.

Step by step solution

01

Understand the Equation

The given equation is an equality between 11 and -q. The goal is to solve for the variable q.
02

Isolate q

To isolate the variable q, we need to get rid of the negative sign in front of q. To do this, we will multiply both sides of the equation by -1.
03

Perform the Multiplication

Multiply both sides of the equation by -1: \[-1 \times 11 = -1 \times (-q)\]This simplifies to: \[-11 = q\]
04

Write the Solution

The solution to the equation is \[q = -11\]

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Key Concepts

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

Isolating Variables
Isolating variables is a fundamental step in solving equations. The goal is to determine the value of the unknown variable by getting it alone on one side of the equation. In our exercise, we started with the equation: \[11 = -q\] We need to isolate the variable \ q. To do this, we look at what is affecting \ q \ and try to undo these operations. In this case, \ q \ is being multiplied by -1. By multiplying both sides of the equation by -1, we can remove -1 from \ q\. This step is crucial because it simplifies the equation and helps in solving for the variable directly.
Integer Operations
Integer operations involve basic arithmetic processes鈥攁ddition, subtraction, multiplication, and division鈥攁pplied to whole numbers, or 'integers.' In the given exercise, we used multiplication.
  • The equation was \(11 = -q\).
  • To isolate \ q, we needed to remove the -1 multiplying it.
  • We did this by multiplying both sides by -1, an integer operation.
This led us to these steps: \[ -1 \times 11 = -1 \times (-q) \] Simplifies to: \[-11 = q\]. Handling integers correctly is vital. Multiplying two integers follows straightforward rules: multiplying a positive and a negative number results in a negative number, and multiplying two negatives gives a positive result.
Multiplication Property of Equality
The multiplication property of equality states that if you multiply both sides of an equation by the same number, the equality holds. This property is useful for isolating variables or simplifying equations. In our equation \[11 = -q\], we used the multiplication property by multiplying both sides by -1. This ensured that we didn't change the equality while isolating \ q. The steps were:
  • Multiply both sides by -1: \(-1 \times 11 = -1 \times (-q)\)
  • This simplifies to \(-11 = q\).
The rule allows us to maintain balance in the equation while simplifying our work to reach the solution \ q = -11.

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