Problem 184 Solve the following equations wi... [FREE SOLUTION]

Chapter 2: Problem 184

Solve the following equations with constants on both sides. $$-12 p-9=9$$

Short Answer

Expert verified

p = -1.5

Step by step solution

Isolate the Variable Term

First, add 9 to both sides of the equation to isolate the term containing the variable. -12p - 9 + 9 = 9 + 9 This simplifies to: -12p = 18

Solve for the Variable

Next, divide both sides of the equation by -12 to solve for p. -12p / -12 = 18 / -12 This simplifies to: p = -3/2 p = -1.5

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Key Concepts

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

Isolating Variable

When solving linear equations, one of the main goals is to isolate the variable. This means we want to get the variable (in this case, $ p $) by itself on one side of the equation.
To do this, follow these simple steps:

Identify which term contains the variable.
Use addition or subtraction to move any constants (numbers without variables) to the other side of the equation.
Remember that whatever you do to one side of the equation, you must do to the other side to maintain balance.

In our example, we started with the equation $-12p - 9 = 9$. The variable term is $-12p$. To isolate it, we added 9 to both sides to cancel out the -9:
$-12p - 9 + 9 = 9 + 9$.
This simplifies to $-12p = 18$, effectively isolating the variable term.

Constants on Both Sides

When you have constants on both sides of an equation, your goal is to move them so that they are on one side only. This often involves basic arithmetic operations.
In our example, the equation $-12p - 9 = 9$ had constants on both sides. To treat this, we needed to perform an operation to eliminate one of the constants:

We identified the constant on the same side as the variable (which was -9).
We used addition to cancel out the -9. By adding 9 to both sides, we were effectively canceling out the -9 on the left side:
$-12p - 9 + 9 = 9 + 9$.

This moved all the constants to the right side, simplifying the equation to $-12p = 18$. Moving constants effectively simplifies your equation and helps you get closer to isolating the variable.

Step-by-Step Algebra

When it comes to solving linear equations, following a step-by-step method can make the process easier to understand and manage.
In our example, we followed these steps:

First, we isolated the variable term by adding 9 to both sides to eliminate the constant on the left. This gave us $-12p = 18$.
Second, we solved for the variable by dividing both sides by -12 to get $ p $ on its own:
$-12p / -12 = 18 / -12$.

This simplifies to $ p = -1.5 $.
Each step had a clear purpose and followed logical operations. By breaking it down, complex-looking equations become more approachable. Practice makes this process feel more natural, and always double-check your work to ensure accuracy.

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91影视

Solve the following equations with constants on both sides. $$-12 p-9=9$$

Short Answer

Step by step solution

Isolate the Variable Term

Solve for the Variable

Key Concepts

Isolating Variable

Constants on Both Sides

Step-by-Step Algebra

One App. One Place for Learning.

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