Answer:
x = 14
Explanation:
1.
Do the arithmetic with fractions:
1/4x -5 = 3/4x -12
-5 = 1/2x -12 . . . . . . . subtract 1/4x
7 = 1/2x . . . . . . . . . add 12
14 = x . . . . . . . . . multiply by 2
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2.
Clear fractions first:
x -20 = 3x -48 . . . . . multiply the given equation by 4
28 = 2x . . . . . . . . add 48-x
14 = x . . . . . . . . divide by 2
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Additional comments
This kind of equation, with variables and constants on both sides, is called a "3-step linear equation." As we showed in the first solution, it takes 3 steps to solve it: (1) put the variable term on one side of the equal sign; (2) put the constant term on the other side of the equal sign; (3) divide by the coefficient of the variable.
The arithmetic is often done with fewer errors if the numbers involved are all integers. That is why you're often told to "clear fractions first" when the coefficients involve fractions. Generally, this is accomplished by multiplying both sides of the equation by the least common denominator of the fractions. (Here, the only denominator is 4.)
In the second solution, we see that putting the variable on one side will involve subtracting x, and putting the constant on the other side will involve adding 48. These two steps can be accomplished at once by adding (48-x) to both sides of the equation.
You may want to choose to leave the variable term on the left side of the equation, and put the constant term on the right. Here, doing that will leave the variable term with a negative coefficient. We have chosen solution methods that leave the variable term with a positive coefficient.