IDNLearn.com: Your trusted source for accurate and reliable answers. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.
Sagot :
To solve the equation [tex]\(12y + d = -19y + t\)[/tex] for [tex]\(y\)[/tex], we can follow these steps:
1. Isolate the terms involving [tex]\(y\)[/tex] on one side of the equation.
[tex]\[ 12y + d = -19y + t \][/tex]
Add [tex]\(19y\)[/tex] to both sides of the equation to move all [tex]\(y\)[/tex] terms to the left side.
[tex]\[ 12y + 19y + d = t \][/tex]
Simplify:
[tex]\[ 31y + d = t \][/tex]
2. Isolate [tex]\(y\)[/tex] by moving the constant term [tex]\(d\)[/tex] to the other side.
Subtract [tex]\(d\)[/tex] from both sides of the equation:
[tex]\[ 31y = t - d \][/tex]
3. Solve for [tex]\(y\)[/tex] by dividing by the coefficient of [tex]\(y\)[/tex], which is 31.
[tex]\[ y = \frac{t - d}{31} \][/tex]
Given this solution, we need to determine which answer choice matches the equation:
A. [tex]\(y = 31(t - d)\)[/tex]
This implies [tex]\(y\)[/tex] is directly multiplied by 31, which is not correct.
B. [tex]\(y = \frac{t - d}{31}\)[/tex]
This is exactly what we found in our step-by-step solution.
C. [tex]\(y = \frac{t + d}{-7}\)[/tex]
This is incorrect as it implies a different expression in terms of [tex]\((t + d)\)[/tex] and a negative divisor.
D. [tex]\(y = -7(t + d)\)[/tex]
This is incorrect as it implies direct multiplication by -7 and a different expression.
Thus, the correct answer is:
[tex]\[ \boxed{B: y = \frac{t - d}{31}} \][/tex]
1. Isolate the terms involving [tex]\(y\)[/tex] on one side of the equation.
[tex]\[ 12y + d = -19y + t \][/tex]
Add [tex]\(19y\)[/tex] to both sides of the equation to move all [tex]\(y\)[/tex] terms to the left side.
[tex]\[ 12y + 19y + d = t \][/tex]
Simplify:
[tex]\[ 31y + d = t \][/tex]
2. Isolate [tex]\(y\)[/tex] by moving the constant term [tex]\(d\)[/tex] to the other side.
Subtract [tex]\(d\)[/tex] from both sides of the equation:
[tex]\[ 31y = t - d \][/tex]
3. Solve for [tex]\(y\)[/tex] by dividing by the coefficient of [tex]\(y\)[/tex], which is 31.
[tex]\[ y = \frac{t - d}{31} \][/tex]
Given this solution, we need to determine which answer choice matches the equation:
A. [tex]\(y = 31(t - d)\)[/tex]
This implies [tex]\(y\)[/tex] is directly multiplied by 31, which is not correct.
B. [tex]\(y = \frac{t - d}{31}\)[/tex]
This is exactly what we found in our step-by-step solution.
C. [tex]\(y = \frac{t + d}{-7}\)[/tex]
This is incorrect as it implies a different expression in terms of [tex]\((t + d)\)[/tex] and a negative divisor.
D. [tex]\(y = -7(t + d)\)[/tex]
This is incorrect as it implies direct multiplication by -7 and a different expression.
Thus, the correct answer is:
[tex]\[ \boxed{B: y = \frac{t - d}{31}} \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.