# 4x − 3 = 4x + 9?

im getting 4x = 4x + 12, but that can't be right

Update:

Solve the equation. (If all real numbers are solutions, enter REALS. Enter EMPTY for the empty set.)

Relevance
• 4x − 3 = 4x + 9

False

• 4x-3=4x+9

=>

-3=9 is false

(by cancelling 4x)

=>

solution set= {  }, an empty set.

• You are right. Now, subtract 4x from both sides, and you will get

0 = 12.

The x is disappeared. Write empty, which means the set of solutions is empty.

• If you subtract 4x from both sides you get to a contradictory statement:

0 = 12

That tells you the original statement has no real solutions and so per the instructions, write EMPTY meaning the set of solutions is empty.

If you want to understand the problem a bit more, you can imagine you have two lines:

4x - 3 and 4x + 9

These would be parallel lines because they have the same slope (4) but different y-intercepts.

Mathematically you can think of the solution in terms of when these lines intersect. If they intersect in 1 point, you have one real solution. If they coincide as the same line, they have infinitely many solutions (all real numbers) and if they are parallel they never intersect (no real solutions, empty set)

EMPTY (no real solutions)

• That step is algebraically correct; but the answer is faulty; as 0 does not equal 12 in this universe.

• Yes, that is right so far. Now subtract 4x from both sides. You get  0 = 12. The x has disappeared. You have a false statement, so there is no solution.

• 4x − 3 = 4x + 9

False

• 4x - 3 = 4x + 9

If you add 3 to both sides, you get:

4x = 4x + 12

Then if you subtract 4x from both sides:

0 = 12

FALSE

You end up with an always false condition.  This means that there are no real solutions to your equation.

• Of course it cannot be right.  Neither can the initial statement be right.  Either you have not copied the non-equation correctly (for it certainly is NOT an "equation"), or you are not telling the whole story.  There isn't any solution as it stands, because it is not an equation.  Where does it come from ?  What have YOU done to it ?

• Or 12=0.  I think you'd better read the question again.