Question

|2у-2|+8=14 ....... плз

Answer 1

$|2y - 2| = 6$
________
2у-2=6
И
2у-2=-6
________
у=4 или у=-2

Answer 2

To solve the equation |2у-2| + 8 = 14, follow these steps:

Step 1: Get rid of the constant term on the left side by subtracting 8 from both sides of the equation: |2у-2| = 14 - 8 |2у-2| = 6

Step 2: Since the absolute value can result in both a positive and negative value, we need to split the equation into two cases and solve for each case.

Case 1: 2у-2 is positive: In this case, the absolute value expression becomes just 2у-2. So, rewrite the equation as 2у-2 = 6.

Now, solve for у: Add 2 to both sides: 2у = 6 + 2 2у = 8

Divide both sides by 2: у = 8 / 2 у = 4

Case 2: 2у-2 is negative: In this case, the absolute value expression becomes -(2у-2). So, rewrite the equation as -(2у-2) = 6.

Now, solve for у: Distribute the negative sign on the left side: -2у + 2 = 6

Subtract 2 from both sides: -2у = 6 - 2 -2у = 4

Divide both sides by -2: у = 4 / -2 у = -2

Step 3: Check the solutions: Now, you should check if the solutions found in both cases satisfy the original equation: For у = 4: |2(4) - 2| + 8 = |8 - 2| + 8 = |6| + 8 = 6 + 8 = 14 (satisfied)

For у = -2: |2(-2) - 2| + 8 = |-4 - 2| + 8 = |-6| + 8 = 6 + 8 = 14 (satisfied)

Both solutions are valid, so the solutions to the equation are у = 4 and у = -2.