Problem 40 Solve. $$ q=\frac{p-r}{2}, \... [FREE SOLUTION]

Chapter 15: Problem 40

Solve. $$ q=\frac{p-r}{2}, \text { for } r $$

Short Answer

Expert verified

r = p - 2q

Step by step solution

Multiply both sides by 2

To isolate the variable, first multiply both sides of the equation by 2 to get rid of the fraction. This results in: ##2q = p - r##.

Rearrange the equation to solve for r

Next, add r to both sides to move r to the left-hand side of the equation. This results in: ##r + 2q = p##.

Solve for r

Subtract 2q from both sides to solve for r: ##r = p - 2q##.

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Key Concepts

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

variable isolation

In algebra, isolating the variable is a crucial step. This means making the variable stand alone on one side of the equation. For instance, if we need to solve for the variable 'r' in the equation given:

$q = \frac{p - r}{2}$,
we first have to isolate 'r'.
Multiply both sides by 2 to clear the fraction. This gives:

2q = p - r.
Now, 'r' is part of the equation on one side, which we need to completely isolate in the next steps. Isolating variables makes equations easier to work with as you progress through the solution.

rearrange equations

Rearranging equations involves shifting terms around while keeping the equation balanced. You add, subtract, multiply, or divide both sides to get the desired variable alone. Continuing with our example:

2q = p - r.
We need 'r' alone on one side. To move 'r' to the other side, add 'r' to both sides:

r + 2q = p.

Now, 'r' is on one side, but it is still mixed with other terms. Properly rearranging terms ensures every step logically follows the last and keeps the equation balanced.

linear algebra

Linear algebra often deals with equations of straight lines and their intersections. Our exercise is a linear equation. A linear equation is one where the highest exponent of the variable is one (hence linear). The equation we have, after step one, is:

2q = p - r.
This is a linear relationship between p, q, and r. Linear algebra simplifies solving relationships like this, which can be visualized as straight lines on a graph.

algebraic manipulation

Algebraic manipulation refers to the process of simplifying and solving equations using operations like addition, subtraction, multiplication, and division. In this example, after rearranging the equation:
r + 2q = p, we perform algebraic manipulation by subtracting 2q from both sides:

r = p - 2q.
This final step isolates 'r' on one side, giving us the solution. Understanding these manipulations is key to simplifying and solving more complex equations.

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91影视

Solve. $$ q=\frac{p-r}{2}, \text { for } r $$

Short Answer

Step by step solution

Multiply both sides by 2

Rearrange the equation to solve for r

Solve for r

Key Concepts

variable isolation

rearrange equations

linear algebra

algebraic manipulation

One App. One Place for Learning.

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