Solve the following equation: [tex]$6 y-20=2 y-4$[/tex].
A. [tex]$y=2$[/tex]
B. [tex]$y=3$[/tex]
C. [tex]$y=16$[/tex]
D. [tex]$y=4$[/tex]
Answer (1)
Subtract 2 y from both sides: 4 y − 20 = − 4 .
Add 20 to both sides: 4 y = 16 .
Divide both sides by 4: y = 4 .
The solution is 4 .
Explanation
Understanding the Problem We are given the equation 6 y − 20 = 2 y − 4 and we need to solve for y .
Isolating y terms First, we want to isolate the terms with y on one side of the equation. To do this, we subtract 2 y from both sides of the equation:
6 y − 20 − 2 y = 2 y − 4 − 2 y
This simplifies to:
4 y − 20 = − 4
Isolating the y term Next, we want to isolate the y term by adding 20 to both sides of the equation:
4 y − 20 + 20 = − 4 + 20
This simplifies to:
4 y = 16
Solving for y Finally, we solve for y by dividing both sides of the equation by 4:
4 4 y = 4 16
This simplifies to:
y = 4
Final Answer Therefore, the solution to the equation 6 y − 20 = 2 y − 4 is y = 4 . The correct answer is D.
Examples
Imagine you're balancing a budget. On one side, you have expenses that depend on a certain number of items you purchase, and on the other side, you have a fixed income. Solving an equation like this helps you determine the number of items you can afford to purchase while keeping your expenses equal to your income. This type of problem is a fundamental concept in algebra and is used in various real-life situations, such as financial planning, resource allocation, and determining break-even points in business.
