If \(\frac{2x}{5y} = 6\), what is the value of \(y\) in terms of \(x\)?

2. \(\frac{11}{4} - a = 3\), what is the value of \(a\) in the equation?

In mathematics, this response explains how to find the value of y in terms of x in an equation and how to determine the value of a in another equation. ;

Answered by harshsi745 | 2024-06-27

For the first equation, in terms of x: y = 15 x ​
For the second equation: a = − 4 1 ​

To solve the given equations step-by-step, we will address them individually.

Solve for y in terms of x from the equation 5 y 2 x ​ = 6

Step 1: Isolate y To isolate y , we will first rearrange the equation:
5 y 2 x ​ = 6
Multiply both sides by 5 y to eliminate the fraction:
2 x = 30 y
Step 2: Solve for y Now divide both sides by 30:
y = 30 2 x ​
This simplifies to:
y = 15 x ​
So the value of y in terms of x is: y = 15 x ​

Solve for a in the equation 4 11 ​ − a = 3

Step 1: Rearranging the equation To find a , we can first isolate it by rearranging the equation:
4 11 ​ − a = 3
Add a to both sides and subtract 3 from both sides:
4 11 ​ − 3 = a
Step 2: Solve for a Now we need to combine the terms on the left. Convert 3 to a fraction with a denominator of 4:
3 = 4 12 ​
Thus:
a = 4 11 ​ − 4 12 ​
This simplifies to:
a = 4 11 − 12 ​ = 4 − 1 ​
So the value of a is: a = − 4 1 ​

Answered by sriLEKHA89 | 2024-08-12

For the equation 5 y 2 x ​ = 6 , the value of y in terms of x is y = 15 x ​ . For the equation 4 11 ​ − a = 3 , the value of a is (a = -\frac{1}{4}.
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Answered by sriLEKHA89 | 2024-09-26