1a-15=4a-3

Question

Why do you subtract 4a from each side?

Answer 1

To solve for a, the best way might be to subtract one a from each side, so that the resulting coefficient of a is positive.

1a-15=4a-3

   -15 = 3a -3; now add 3 to each side:

   -12 = 3a

Now divide each side by 3:  -4 = a.

 

An advantage to this idea is that, when solving INEQUALITIES, one avoids division by a negative coefficient. Example:

 a-15 ≤ 4a-3

   -15 ≤ 3a - 3

  -12 ≤ 3a

  -4 ≤ a.  Reading this aloud, we read from right to left: a IS GREATER THAN OR EQUAL TO -4.  (We do this because the natural 'subject' of this solution, a, appears on the right side.)  

Answer 2

It is possible that you are a "thinking" student, so I will offer a thoughtful answer.

 

To "solve" means to find the value(s) of the variable for which the equation (or inequality) is true.  That means we need to get "a=" (or else, "=a) somehow.

 

The rule is that adding (or subtracting or dividing or multiplying) equals by equals produces equals.  Our strategy will be to find a single operation and perform the opposite operation on the equation.

 

So, with the equation 1a-15=4a-3, we could either (a) subtract 1a from both sides, (b) add 15 to both sides, (c) subtract 4a from both sides, or (d) add 3 to both sides. 

 

After some consideration, let's subtract 1a from both sides:

     -15 = 3a - 3

  Just to show how this works, let's use the Distributive Property and factor out 3 on the right side:

      -15 = 3(a - 1)

  O.K., when we divide by 3, we get:

      -5 = a - 1

  Then adding 1 to both sides:

      -4 = a

  Of course, that can be written as:

       a = -4

 

What is the lesson??  Well, after "studying" many problems, you might find an easier or quicker process to isolate the variable in the equation and thus solve for it.  Until that time, use the straight-forward and obvious method of getting the variable on the left side.

Answer 3

you subtract 4a from each side so as get both "a" terms on the left side, so that they can then be combined:

 

 

a - 15 = 4a - 3 ---> a - 4a - 15 = -3;  or, -3a - 15 = -3;  then add 15 to each side ---> -3a = -3 + 15 = 15 - 3 = 12;

 

 then divide each side by -3 ---> a = 12/(-3 )= -4