Is it possible to solve |2x| + 3 =x?
I got x= -3, but it doesn't seem to work when you plug it into the original equation to check it..
|2(-3)| + 3 = -3
9=-3
?
|2x| = x-3
2x= x-3 or -2x = x-3
x = -3 which was your answer OR -3x = -3 ---> x = 1
But ... neither answer satisfies the original equation, so there is no solution.
thanks
To solve the equation |2x| + 3 = x, we can follow these steps:
Step 1: Split the equation into two cases:
Case 1: 2x + 3 = x (when 2x is positive or zero)
Case 2: -2x + 3 = x (when 2x is negative)
Step 2: Solve each case separately.
Case 1:
In this case, we have 2x + 3 = x.
Subtract x from both sides: 2x - x + 3 = 0.
Simplify: x + 3 = 0.
Subtract 3 from both sides: x = -3.
Case 2:
In this case, we have -2x + 3 = x.
Add 2x to both sides: 3 = x + 2x.
Combine like terms: 3 = 3x.
Divide both sides by 3: x = 1.
So, when solving the equation, we obtain two possible solutions: x = -3 and x = 1.
Now, let's check if these solutions satisfy the original equation:
For x = -3: |2(-3)| + 3 = -3.
|-6| + 3 = -3.
6 + 3 = -3.
9 ≠ -3.
Therefore, x = -3 is not a solution to the original equation.
For x = 1: |2(1)| + 3 = 1.
|2| + 3 = 1.
2 + 3 = 1.
5 ≠ 1.
Therefore, x = 1 is also not a solution to the original equation.
Hence, there are no solutions to the equation |2x| + 3 = x.