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Chapter 8: Problem 100

Solve.$$4-5 y=3$$

Short Answer

Expert verified
The solution is \( y = \frac{1}{5} \).

Step by step solution

01

Isolate the Variable Term

To begin solving the equation, we need to isolate the term that contains the variable. Start by subtracting 4 from both sides of the equation:given: \[4 - 5y = 3\]Subtract 4 from both sides:\[4 - 5y - 4 = 3 - 4\]This simplifies to:\[-5y = -1\]
02

Solve for the Variable

Now we need to solve for the variable \(y\). Since \(-5y = -1\), we divide both sides of the equation by \(-5\):\[-5y / -5 = -1 / -5\]This simplifies to:\[y = \frac{1}{5}\]

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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 an essential skill in algebra. It helps us simplify equations to find the value of the unknown.
To isolate a variable means to get the variable by itself on one side of the equation.
Here is how you do it in steps:
  • Identify the term that contains the variable.
  • Remove any other terms from that side by performing the inverse operation.
For example, in the equation \(4 - 5y = 3\), the term with the variable is \(-5y\).
We need to move the \(4\) to the other side by subtracting 4 from both sides, like so: \[4 - 5y - 4 = 3 - 4\]
This simplifies to \(-5y = -1\).
Now the term with the variable is isolated, and we are ready for the next step.
Solving for y
Once the variable term is isolated, the next step is to solve for the variable itself.
This often involves dividing or multiplying both sides of the equation to get the variable alone.
In our example, we have \(-5y = -1\).
  • To solve for \(y\), we need to divide both sides by \(-5\).
  • This operation cancels out the coefficient of \(y\) on the left side.
Here鈥檚 how it looks: \[-5y / -5 = -1 / -5\]
This simplifies further to: \ y = \frac{1}{5} \
Now, we have the value of \(y\), which is \ \frac{1}{5} \.
Basic Algebra
Understanding basic algebra is key to solving equations and many other types of math problems.
Some of the core principles include:
  • Performing arithmetic operations such as addition, subtraction, multiplication, and division.
  • Applying the inverse operations to both sides of an equation to keep it balanced.
Consider the equation \(4 - 5y = 3\) again.
The process begins with identifying and isolating the variable term, followed by solving for that variable.
It鈥檚 important to practice these steps to build a solid foundation in algebra.
Remember:
  • Each operation performed on one side of the equation must be done to the other side.
  • This ensures the equation remains balanced and the solution is accurate.
By mastering these basic algebra techniques, solving equations becomes a straightforward and logical process.

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