Solve the equation for the indicated variable:

(ax+b)/(cx+d)=6 , Solve for X

pre-cal? Try Algebra I

(ax+b)/(cx+d) = 6
ax+b = 6(cx+d)
ax+b = 6cx+6d
ax-6cx = 6d-b
(a-6c)x = 6d-b
x = (6d-b)/(a-6c)

Thank you Mr. Steve

To solve the equation (ax + b)/(cx + d) = 6 for x, we need to isolate x on one side of the equation. Here's how:

1. Start by cross-multiplying, which means multiplying both sides of the equation by (cx + d) to eliminate the denominator:

(ax + b)/(cx + d) * (cx + d) = 6 * (cx + d)

This simplifies to:

ax + b = 6(cx + d)

2. Distribute 6 to both terms inside the parentheses:

ax + b = 6cx + 6d

3. Next, distribute a to the terms on the left side:

ax + b = 6cx + 6d

becomes

ax + b = 6cx + 6d

4. Now, let's gather all the terms with x on one side of the equation. To do this, subtract 6cx from both sides:

ax + b - 6cx = 6cx + 6d - 6cx

This simplifies to:

ax - 6cx + b = 6d

5. Factor out x from the left side of the equation:

x(a - 6c) + b = 6d

6. Finally, divide both sides of the equation by (a - 6c) to solve for x:

x(a - 6c) + b = 6d

The final equation is:

x = (6d - b)/(a - 6c)

Therefore, the solution for x is (6d - b)/(a - 6c).