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Chapter 2: Problem 13

Fill in the Blanks To solve \(A=p+i\) for \(p\) _____ \(i\) from both sides.

Short Answer

Expert verified
Subtract

Step by step solution

01

Identify the equation

The given equation is \(A=p+i\). In order to isolate \(p\), we need to manipulate the equation.
02

Subtract Variable

Subtract \(i\) from both sides of the equation, doing so guarantees the equation remains balanced while isolating the variable \(p\).
03

Result

The variable \(p\) is now isolated on one side of the equation, and the result is \(p = A - i\).

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Key Concepts

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

Isolate Variable
Isolating a variable in an equation is a fundamental skill in algebra that allows us to find the value of that variable. If we have an equation like A = p + i, and we want to solve for p, we need to get p by itself on one side of the equal sign. That means we need to move all other terms to the opposite side.

Think of the equation as a balance scale鈥攚hatever we do to one side, we must do to the other to keep things equal. In the exercise you have with A = p + i, subtracting i from both sides is the key to isolating p. This step is all about making the variable of interest the 'star of the show', giving it its own space, without any other terms around it.
Equation Manipulation
Equation manipulation involves various operations that help us modify and solve algebraic equations. When we manipulate an equation, we're rearranging it in a way that makes it easier to understand or solve, while keeping the equation equal, or 'balanced', as it's often described.

Common Manipulations

  • Adding or Subtracting: To move a term from one side of an equation to the other, you add or subtract it from both sides.
  • Multiplying or Dividing: To solve for a coefficient or to simplify the equation, you might multiply or divide terms on both sides.
  • Distributing: Sometimes you need to get rid of parentheses, and that's when you use the distributive property.

These techniques can be utilized individually or in combination to systematically break down an equation and solve for a desired variable. They are the building blocks of algebra and essential for solving more complex mathematical problems.
Subtracting Terms
Subtracting terms is an equation manipulation strategy used to simplify expressions and solve equations. When faced with an equation like A = p + i, and we want to find the value of p, we will subtract i from both sides of the equation. This action helps to 'cancel out' the i on the same side as p, effectively moving it to the other side.

It's important to subtract the term exactly as it appears. If i is positive, we subtract positive i. In doing so, we are applying the inverse operation to both sides of the equation, ensuring that the equation stays balanced and that the integrity of the original equation remains intact.

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Most popular questions from this chapter

The volume \(V\) of a cone is given by the formula \(V=\frac{1}{3} \pi r^{2} h .\) Solve the formula for \(h\), and then calculate the height \(h\) if \(V\) is \(36 \pi\) cubic inches and the radius \(r\) is 6 inches.

List as many types of angles as you can think of. Then define each type.

s One investment pays \(8 \%\) and another pays \(11 \% .\) If equal amounts are invested in each, the combined interest income for 1 year is \(\$ 712.50 .\) How much is invested at each rate?

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Explain why multiplying both sides of an inequality by a negative constant reverses the direction of the inequality.
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