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Chapter 2: Problem 143

Translate to an equation and then solve. 133 is the product of -19 and \(n .\)

Short Answer

Expert verified
n = -7

Step by step solution

01

- Translate the Statement to an Equation

The problem states that 133 is the product of -19 and a number n. We can translate this into an equation by writing: 133 = -19n
02

- Isolate the Variable

To find the value of n, we need to isolate it on one side of the equation. We do this by dividing both sides of the equation by -19: \( n = \frac{133}{-19} \)
03

- Calculate the Value of n

Perform the division to find the value of n: \( n = \frac{133}{-19} = -7 \)

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Key Concepts

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

Translating Word Problems to Equations
Word problems in math often describe a scenario using words, and it's important to translate these words into mathematical equations. In this exercise, the problem tells us that 133 is the product of -19 and a number. To translate this, we identify the key terms:
  • '133' is the result, so it will be on one side of the equation.
  • 'Product of -19 and a number' indicates multiplication, with -19 being multiplied by an unknown number, which we can call n.
Thus, the statement '133 is the product of -19 and n' can be written as:
\[ 133 = -19n \] This step is crucial because correctly translating the words into math ensures we solve the problem accurately.
Isolating Variables
Once you have the equation, the next step is to isolate the variable you need to solve for. In our example, we need to find the value of n. To do this, the variable n must be by itself on one side of the equation. Our equation from the translation step is:
\[ 133 = -19n \] To isolate n, we need to eliminate the coefficient -19. We do this by doing the opposite operation. Since -19 is multiplied by n, we'll divide both sides of the equation by -19:
\[ n = \frac{133}{-19} \] This method works for any equation; just perform the opposite operation to isolate the variable.
Division in Algebra
Division often plays an essential role in solving algebraic equations, especially when you are isolating variables. In our example, we isolated the variable n by dividing both sides by -19. The equation was:
\[ n = \frac{133}{-19} \] Now, let's perform the division to get the value of n:
\[ n = -7 \] Dividing 133 by -19 gives us -7. Therefore, n equals -7.
Remember, when dividing two numbers with opposite signs, the result is negative. Practice dividing different numbers to get comfortable with this concept. It's a powerful tool for solving many algebraic equations.

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