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Chapter 2: Problem 73

Explain what it means to solve a formula for a variable.

Short Answer

Expert verified
Solving a formula for a variable means getting that variable alone on one side of the equation. This is done by performing operations that won't change the balance of the equation. In this case, we successfully isolated \(x\) by dividing both sides of the equation by \(a\), hence \(x = \frac{b}{a}\).

Step by step solution

01

Understanding the Problem

Firstly, to solve a formula for a variable means to manipulate the formula so that the variable is on one side of the equation and everything else is on the other side. Essentially, the aim here is to make the formula illustrate how to calculate the value of the variable in terms of the other variables or constants. Let's consider the formula \(ax = b\), and we are to solve for \(x\).
02

Isolate the Variable

To get \(x\) alone, we need to eliminate \(a\) from the left side of the equation. We do this by using fundamental operations that keep the equation balanced. Since \(a\) is being multiplied by \(x\), we can get rid of \(a\) by doing the opposite, that is, dividing both sides of the equation by \(a\). This gives us \(x = \frac{b}{a}\).
03

Interpreting the Result

Now, \(x\) has been isolated on one side of the equation. This means we have solved the equation for \(x\), and \(x\) can now be calculated if the values of \(b\) and \(a\) are known.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. In a film, the actor Charles Coburn played an elderly "uncle" character criticized for marrying a woman when he is 3 times her age. He wittily replies, "Ah, but in 20 years time I shall only be twice her age." How old is the "uncle" and the woman?

When solving an inequality, when is it necessary to change the direction of the inequality symbol? Give an example.

Solve each inequality. $$3 x+1 \leq 3(x-2)$$

In an inequality such as \(5 x+4<8 x-5,\) I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

Can a triangle contain two \(90^{\circ}\) angles? Explain your answer.
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