Solving Linear Equations: Inverse Method

Step 1: Identify the Variable
In this equation, the variable is x.

Step 2: Identify the Operations
The operations in this equation are division and subtraction.

Step 3: Isolate the Variable
To isolate the variable, we need to undo the operations in the reverse order that they were applied. We will first undo the division by multiplying both sides by the LCD, which is 12.
x/4 x/6 = x-7
(12/4)x(12/6)x = 12(x-7)
3x2x = 12x-84

Next, we will undo the subtraction by adding 84 to both sides.
3x2x + 84 = 12x-84 + 84
3x2x + 84 = 12x
3x2x - 12x = -84
x(3x-12) = -84

Finally, we will divide both sides by (3x-12) to isolate x.
x(3x-12)/(3x-12) = -84/(3x-12)
x = -28/(x-4)

Step 4: Check Your Answer
To check our answer, we need to substitute x = -28/(x-4) back into the original equation and see if both sides are equal.
x/4 x/6 = x-7
(-28/(x-4))/4 (-28/(x-4))/6 = -28/(x-4)-7
-7/(x-4) - 14/(x-4) = -28/(x-4)-7
-21/(x-4) = -21/(x-4)

Conclusion
Therefore, the solution to the equation x/4 x/6=x-7 is x = -28/(x-4).