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Chapter 3: Problem 51

Solve the equation. $$5=\frac{y}{-3}$$

Short Answer

Expert verified
y = -15

Step by step solution

01

Understand the equation

The equation given is \(5 = \frac{y}{-3}\). This means that 5 is equal to \(y\) divided by -3.
02

Isolate the variable y

To isolate \(y\), multiply both sides of the equation by -3 to cancel the denominator: \(5 \times (-3) = \frac{y}{-3} \times (-3)\).
03

Simplify

Perform the multiplication on both sides: \(5 \times (-3) = -15\)This simplifies to \(y = -15\).

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Key Concepts

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

Isolating the Variable
When solving linear equations, one of the main goals is to isolate the variable. This step helps us to find the value of the unknown variable by itself. In our example, the variable is 'y' in the equation: \[5 = \frac{y}{-3}\].

The variable 'y' is divided by -3. To isolate 'y', we need to get rid of the -3.

We do this by performing the opposite operation, which is multiplication. Therefore, we multiply both sides of the equation by -3.
Multiplication of Integers
Understanding multiplication with integers is crucial. Integer multiplication involves multiplying positive and negative numbers.

Here are key rules to remember:
  • Multiplying two positive numbers results in a positive number.
  • Multiplying two negative numbers also results in a positive number.
  • Multiplying a positive number by a negative number results in a negative number.
In our problem: \[5 \times (-3)\] we multiply a positive and a negative number, resulting in \(-15\).
Equation Simplification
Equation simplification helps to make equations easier to solve. We simplify by combining like terms and performing basic arithmetic operations.

In our example, after multiplying both sides by -3, we simplify \(5 \times (-3)\) to get \(-15\).
Now, the equation is: \(y = -15\).

At this point, the equation is simplified and 'y' has been isolated, making it easier to understand the solution.
Basic Algebra
Basic algebra involves understanding and manipulating algebraic expressions and equations. It often includes working with variables, constants, and performing operations like addition, subtraction, multiplication, and division.

Our exercise demonstrates basic algebra steps:
  • Identifying the equation \(5 = \frac{y}{-3}\)
  • Isolating the variable 'y' by multiplying both sides by -3
  • Simplifying the result to find \(y = -15\)
These steps show how foundational skills in algebra work together to solve equations.

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