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).