2|x+2|-1=5
To solve the equation 2|x+2|-1=5, we can start by isolating the absolute value term by adding 1 to both sides:
2|x + 2| = 6
Next, we can divide both sides by 2 to get:
|x + 2| = 3
Now we have two possible cases to consider:
Case 1: x + 2 is positive:
In this case, the absolute value term remains unchanged. So we have:
x + 2 = 3
Solving for x, subtract 2 from both sides:
x = 1
Case 2: x + 2 is negative:
In this case, the absolute value term changes the sign. So we have:
-(x + 2) = 3
Expanding the negative sign:
-x - 2 = 3
Solving for x, add 2 to both sides:
-x = 5
Multiply both sides by -1 (to get a positive x):
x = -5
So the solutions to the equation 2|x+2|-1=5 are x = 1 and x = -5.
To solve the equation 2|x+2|-1=5, follow these steps:
Step 1: Move the constant term to the other side of the equation:
2|x+2| = 5 + 1
Step 2: Simplify the right side:
2|x+2| = 6
Step 3: Divide both sides of the equation by 2 to isolate the absolute value expression:
|x+2| = 6/2
Step 4: Simplify the right side:
|x+2| = 3
Step 5: Set up two separate equations, one with the positive value and one with the negative value of the absolute value expression:
Case 1: x+2 = 3 (positive value)
Case 2: x+2 = -3 (negative value)
Step 6: Solve each equation separately:
Case 1:
x+2 = 3
Subtract 2 from both sides:
x = 3 - 2
x = 1
Case 2:
x+2 = -3
Subtract 2 from both sides:
x = -3 - 2
x = -5
Step 7: Write down the solutions:
The solutions to the equation 2|x+2|-1=5 are x = 1 and x = -5.