Question

|x-1|=x хелп плиаз!!!!!!

Answer 1

Решение на фото!!!!!!!!!

Answer 2

Sure, I'd be happy to help you solve the equation |x-1| = x. Let's go through the steps to find the solution:

Step 1: Split the equation into two cases based on the absolute value:

Case 1: (x-1) = x Case 2: -(x-1) = x

Step 2: Solve each case separately:

Case 1: (x - 1) = x Let's solve for x: x - 1 = x To isolate x, let's get rid of the -1 by adding 1 to both sides: x - 1 + 1 = x + 1 x = x + 1

At this point, we notice that the x cancels out on both sides, and we are left with: 0 = 1

However, 0 can never be equal to 1, so there is no solution in this case.

Case 2: -(x - 1) = x Let's solve for x:

• (x - 1) = x To isolate x, let's first distribute the negative sign:
• x + 1 = x Now, let's move all the terms with x to one side and constants to the other side:
• x - x = -1 -2x = -1

Now, divide both sides by -2 to solve for x: x = -1 / -2 x = 1/2

Step 3: Check the solution: Now, we need to check if x = 1/2 satisfies the original equation |x - 1| = x:

|x - 1| = |1/2 - 1| = |-1/2| = 1/2

So, the solution x = 1/2 satisfies the original equation.

Step 4: Final Answer: The solution to the equation |x-1| = x is x = 1/2.

Remember that we had two cases initially, but Case 1 had no solution, so the only valid solution for the given equation is x = 1/2.