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

Problem

(a*x+b)/(c*x+d)=6

Solution

1. Multiply both sides of the equation by the denominator c*x+d to clear the fraction.

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

2. Distribute the constant 6 into the terms inside the parentheses.

a*x+b=6*c*x+6*d

3. Rearrange the equation to collect all terms containing x on one side and all other terms on the opposite side.

a*x−6*c*x=6*d−b

4. Factor out the common variable x from the left side of the equation.

x*(a−6*c)=6*d−b

5. Isolate x by dividing both sides by the expression (a−6*c)

x=(6*d−b)/(a−6*c)

Final Answer

(a*x+b)/(c*x+d)=6⇒x=(6*d−b)/(a−6*c)

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