Answer:
x = -3
Explanation:
You are asked to solve the 3-step linear equation -6x -4 = -10x -16.
Solution
Step 1 is collect the variable terms on one side of the equal sign. You may find it convenient to add the opposite of the variable term that has the lowest coefficient.
-6x -4 +10x = -10x -16 +10x . . . . . . add 10x to both sides
4x -4 = -16 . . . . . . . . . . . . . . . simplify
Step 2 is to isolate the variable term by adding the opposite of any constant term on the same side of the equal sign.
4x -4 +4 = -16 +4 . . . . . . . . add 4 to both sides
4x = -12 . . . . . . . . . . . . simplify
Step 3 is to isolate the variable by dividing by its coefficient.
(4x)/4 = (-12)/4 . . . . . . . divide both sides by 4
x = -3 . . . . . . . . . . . . simplify
The value of x is -3.
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Additional comments
Avoiding errors
By choosing to add 10x rather than 6x in step 1, we ensure the coefficient of x is positive. Having a positive coefficient for the variable tends to reduce errors.
If we added 6x instead, the equation going into step 3 would be 12 = -4x, so we would have x = 12/-4. Dividing by negative numbers sometimes causes confusion, so we try to avoid it.
We notice after step 1 that all of the numbers in the equation are divisible by 4, the coefficient of x. We could divide by 4 at that point to get ...
x -1 = -4
Then adding 1 gives the solution:
x = -3
In short, the steps described above offer guidance to suggest what you can do if you don't see a simpler way.
Alternate solution steps
Another way any linear equation can be solved is to ...
- subtract one side to give an equation in "general form":
something = 0. - divide by the coefficient of x
- add the opposite of the remaining constant
Again, choosing to subtract the side of the equation with the lowest x-coefficient can be helpful in the end.
-6x -4 -(-10x -16) = 0 . . . . . . subtract the right side from both sides
4x +12 = 0 . . . . . simplify
x +3 = 0 . . . . . . . divide by the x-coefficient
x = -3 . . . . . . . . . add the opposite of the constant
Rule of equality
It is extremely important to understand that whatever you do to one side of the equation must also be done to the other side. When we say "add -3" we always mean "add -3 to both sides of the equation." (This is the foundation of Algebra, and is what allows you to solve equations of all kinds.)