Select the correct answer.
Which equation is correctly rewritten to solve for [tex]$y$[/tex]?
[tex]$12 y+d=-19 y+t$[/tex]
A. [tex]$y=-7(t+d)$[/tex]
B. [tex]$y=\frac{t+d}{-7}$[/tex]
C. [tex]$y=31(t-d)$[/tex]
D. [tex]$y=\frac{t-d}{31}$[/tex]
Answer (2)
Add 19 y to both sides: 31 y + d = t .
Subtract d from both sides: 31 y = t − d .
Divide both sides by 31 : y = 31 t − d .
The correct answer is y = 31 t − d .
Explanation
Understanding the Problem We are given the equation 12 y + d = − 19 y + t and we want to solve for y . This means we want to isolate y on one side of the equation.
Adding 19y to Both Sides First, we add 19 y to both sides of the equation to get all the y terms on one side: 12 y + 19 y + d = − 19 y + 19 y + t 31 y + d = t
Subtracting d from Both Sides Next, we subtract d from both sides of the equation to isolate the term with y :
31 y + d − d = t − d 31 y = t − d
Dividing by 31 Finally, we divide both sides of the equation by 31 to solve for y :
31 31 y = 31 t − d y = 31 t − d
Selecting the Correct Answer Comparing our result with the given options, we see that option D, y = 31 t − d , is the correct answer.
Examples
Solving for a variable is a fundamental skill in algebra and is used in many real-world applications. For example, imagine you are trying to determine how many hours you need to work to earn a certain amount of money. If you know your hourly wage and have an equation that relates your earnings to the number of hours worked, you can solve for the number of hours needed. This skill is also crucial in fields like physics, engineering, and economics, where equations are used to model and solve problems.
To solve the equation 12 y + d = − 19 y + t for y , we found that y = 31 t − d . The correct answer from the options given is option D. This process involved isolating y by moving terms and simplifying the equation step-by-step.
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