If 24 - 7x = 3y, find the value of x in terms of y.

To find the value of \( x \) in terms of \( y \) given the equation:

\[ 24 - 7x = 3y \]

we will isolate \( x \). Here are the steps:

1. Subtract 24 from both sides of the equation to move the constant term to the right side:
   \[
   24 - 7x - 24 = 3y - 24
   \]
   Simplifying this, we get:
   \[
   -7x = 3y - 24
   \]

2. Divide both sides of the equation by \(-7\) to solve for \( x \):
   \[
   x = \frac{3y - 24}{-7}
   \]

3. To make the expression simpler, we can distribute the negative sign in the denominator:
   \[
   x = -\frac{3y}{7} + \frac{24}{7}
   \]

Thus, the value of \( x \) in terms of \( y \) is:
\[ 
x = \frac{24 - 3y}{7} 
\]

Would you like a detailed explanation of any step, or do you have any further questions?

Here are 8 related questions for further practice:

1. If \( 5x + 3 = 2y \), find the value of \( x \) in terms of \( y \).
2. Solve for \( y \) in terms of \( x \) from the equation \( 4y - 9x = 12 \).
3. If \( 2a + 3b = 5 \), express \( a \) in terms of \( b \).
4. Solve for \( z \) in terms of \( w \) from the equation \( 7z - 4w = 28 \).
5. If \( 3m - 2n = 8 \), find \( m \) in terms of \( n \).
6. Solve for \( k \) in terms of \( j \) from \( 6k + 5j = 15 \).
7. If \( 9p - 2q = 18 \), express \( p \) in terms of \( q \).
8. Solve for \( t \) in terms of \( r \) from \( 5t + 4r = 20 \).

**Tip:** When solving for one variable in terms of another, always aim to isolate the desired variable on one side of the equation. This often involves performing inverse operations such as addition, subtraction, multiplication, or division.

Learn how to solve the equation 24 - 7x = 3y to find the value of x in terms of y with a step-by-step solution. This problem covers linear equations and isolating variables, suitable for students in Grades 7-9.

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