Question

step by step how would you solve 2 | X - 5 | = -5

Answer 1

To solve the equation 2|X - 5| = -5, we need to divide the problem into two cases depending on the value of the absolute value expression.
Case 1: X - 5 is positive or zero
In this case, the absolute value expression |X - 5| is equal to X - 5. We can rewrite the equation with this knowledge:

2(X - 5) = -5

Step 1: Distribute the 2 on the left-hand side:
2X - 10 = -5

Step 2: Add 10 to both sides to isolate the variable:
2X = 5

Step 3: Divide both sides by 2 to solve for X:
X = 5/2 or X = 2.5

Case 2: X - 5 is negative
In this case, the absolute value expression |X - 5| is equal to -(X - 5) or -X + 5. We can rewrite the equation with this knowledge:

2(-X + 5) = -5

Step 1: Distribute the 2 on the left-hand side:
-2X + 10 = -5

Step 2: Subtract 10 from both sides to isolate the variable:
-2X = -15

Step 3: Divide both sides by -2 to solve for X:
X = 15/2 or X = 7.5

So the solution to the equation 2 | X - 5 | = -5 is X = 2.5 or X = 7.5.