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Chapter 2: Problem 53

Solve using the multiplication principle. Don't forget to check! $$ \frac{y}{-8}=11 $$

Short Answer

Expert verified
y = -88

Step by step solution

01

- Identify the equation

The given equation is \( \frac{y}{-8} = 11 \).
02

- Apply the multiplication principle

To isolate \( y \), multiply both sides of the equation by \( -8 \). This gives: \( -8 \cdot \frac{y}{-8} = 11 \cdot -8 \).
03

- Simplify the left side

On the left side, \( -8 \cdot \frac{y}{-8} \) simplifies to \( y \) because the \( -8 \) and \( -8 \) cancel each other out. This results in: \( y = -88 \).
04

- Check the solution

Substitute \( y = -88 \) back into the original equation to verify it solves the equation: \( \frac{-88}{-8} = 11 \). Since \( 11 = 11 \), the solution is correct.

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Key Concepts

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

solving equations
Solving equations involves finding the value of the variable that makes the equation true. In this problem, you need to solve for the variable \( y \) in the equation \( \frac{y}{-8} = 11 \). This equation states that when \( y \) is divided by \( -8 \), the result is 11. To solve for \( y \), we need to isolate it on one side of the equation. The multiplication principle will help us do that. This principle tells us that if we multiply both sides of an equation by the same number, the equation remains true. For this reason, we need to multiply both sides by \( -8 \) to isolate \( y \).
algebraic techniques
Algebraic techniques are methods or strategies used to manipulate and solve equations. One common technique is the multiplication principle.
This technique is useful for solving equations that contain fractions or division. Let's break down the steps used in the solution:

  • Given the equation: \( \frac{y}{-8} = 11 \)
  • To remove the fraction, multiply both sides by \( -8 \).
  • This results in: \( -8 \cdot \frac{y}{-8} = 11 \cdot -8 \)
  • On the left side, the \( -8 \) terms cancel each other out, simplifying to \( y \).
  • This results in \( y = -88 \).
  • Thus, through the multiplication principle, we find that \( y = -88 \).

Using this principle makes it easier to isolate the variable and solve the equation step-by-step.
checking solutions
After solving an equation, it's important to check the solution to ensure it's correct. This is done by substituting the solution back into the original equation and verifying that both sides are equal.

In this case, we found \( y = -88 \). To check if this solution is accurate, substitute \( -88 \) back into the original equation:

\( \frac{-88}{-8} = 11 \).

Simplify the left side:
\( \frac{-88}{-8} = 11 \).

Since \( 11 = 11 \) holds true, the solution \( y = -88 \) is correct.

Always remember to check your work. This practice verifies your solution and helps you catch any potential mistakes.

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. On July 1, Garrett's Pond was \(25 \mathrm{ft}\) deep. since that date, the water level has dropped \(\frac{2}{3} \mathrm{ft}\) per week. For what dates will the water level not exceed \(21 \mathrm{ft} ?\)

Graph the solutions of \(|x|<3\) on the number line.

Use an inequality and the five-step process to solve each problem. Aiden can be paid for his masonry work in one of two ways: Plan \(A: \quad \$ 300\) plus \(\$ 9.00\) per hour Plan \(B:\) Straight \(\$ 12.50\) per hour. Suppose that the job takes \(n\) hours. For what values of \(n\) is plan B better for Aiden?

Translate to an inequality. A number is less than \(10 .\)

Write a problem for a classmate to solve. Devise it so that the problem can be translated to the equation \(x+(x+2)+(x+4)=375\)
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