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Chapter 5: Problem 20

Solve the equations. $$\frac{y}{-8.1}=-1.5$$

Short Answer

Expert verified
y = 12.15

Step by step solution

01

Identify the equation

The given equation is \(\frac{y}{-8.1} = -1.5\)
02

Isolate the variable

To solve for \(y\), multiply both sides of the equation by \(-8.1\). This eliminates the fraction. So, \(\frac{y}{-8.1} \times -8.1 = -1.5 \times -8.1\).
03

Simplify the equation

Simplify the right side of the equation. \(-1.5 \times -8.1 = 12.15\). So, \(y = 12.15\).

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Key Concepts

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

Isolating Variables
Isolating variables is a crucial step in solving linear equations. It means getting the variable you are solving for alone on one side of the equation. This helps in evaluating the unknown value more clearly.
  • First, you observe the equation and identify which variable needs to be isolated.
  • Then, use mathematical operations such as addition, subtraction, multiplication, or division to move other terms to the opposite side of the equation.
Let's look at an example based on the given equation.
  • Starting with \(\frac{y}{-8.1} = -1.5\), you aim to isolate y.
  • Since y is divided by -8.1, you can multiply both sides by -8.1 to cancel out the fraction.
This isolating step sets up the equation for straightforward calculation in the next steps.
Multiplying Fractions
Multiplying fractions can simplify equations effectively. Instead of working with complicated fractions, you can multiply both sides of the equation by a denominator. This helps to clear the fraction and makes the equation easier to manage.
  • When dealing with \(\frac{y}{-8.1} = -1.5\), you multiply both sides by -8.1.
  • This step involves basic multiplication: \(\frac{y}{-8.1} \times -8.1\) on the left side and \(-1.5 \times -8.1\) on the right.
  • This multiplication solves the fraction, making it easier to isolate the variable y.

Fractions disappearing into simpler terms makes solving linear equations more manageable.
Simplifying Equations
Simplifying equations helps find the variable's value in a more straightforward manner. After multiplying and isolating the variable, the next step is to simplify the resulting equation.
  • For example, after isolating y in \(\frac{y}{-8.1} \times -8.1 = -1.5 \times -8.1\), the equation becomes y = -1.5 \times -8.1.
  • Multiply the values on the right side.
  • Here, \(-1.5 \times -8.1 = 12.15\).
Thus, y = 12.15.
Ensure you're careful with signs and multiplication; they can change the result significantly.

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