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Chapter 2: Problem 185

Solve the following equations with constants on both sides. $$-14 q-2=16$$

Short Answer

Expert verified
q = -\frac{9}{7}

Step by step solution

01

- Isolate the variable term

First, we need to isolate the term containing the variable. We do this by moving the constant term from the left-hand side of the equation to the right-hand side. Add 2 to both sides: \[-14q - 2 + 2 = 16 + 2\] This simplifies to: \[-14q = 18\]
02

- Solve for the variable

Now that we have isolated the variable term, divide both sides by -14 to solve for \(q\): \[q = \frac{18}{-14}\] This further simplifies to: \[q = -\frac{9}{7}\]

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Key Concepts

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

isolating variables
When solving linear equations, the goal is often to isolate the variable term on one side of the equation. This allows us to solve for the variable more easily.
In our exercise, we started with the equation \(-14q-2=16\).
Isolating the variable involves moving the constant term to the other side of the equation. To do this, we add 2 to both sides:
\(-14q - 2 + 2 = 16 + 2\)
This cancels out the -2 on the left side, simplifying the equation to:
\(-14q = 18\)
Now, the variable term \(-14q\) is isolated, setting us up to solve for \(q\).
constants on both sides
When constants appear on both sides of the equation, separating the variable from the constants is key. In our example, we have the equation \(-14q - 2 = 16\).
Here, -2 is the constant on the left side, and 16 is the constant on the right side. The process involves moving the constants to one side and the variable to the other.
This is done by performing operations like addition or subtraction to both sides of the equation. We added 2 to both sides to remove the constant term from the left:
\(-14q - 2 + 2 = 16 + 2\)
It simplified the equation and helped us isolate the variable term. Always perform the same operation on both sides to maintain balance in the equation.
solving for a variable
Once we have isolated the variable term, we can solve for the variable itself. In our simplified equation \(-14q = 18\), the next step is to make \(q\) the subject of the formula.
We accomplish this by dividing both sides of the equation by the coefficient of the variable, which is -14 in this case:
\(q = \frac{18}{-14}\)
This simplifies further to:
\(q = -\frac{9}{7}\)
So, solving for the variable \(q\) involves isolating it first, and then using basic arithmetic operations like division to find its value. This step by step approach helps in systematically arriving at the solution.

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