solve the absolute value equation |2×+3|=3
To solve the absolute value equation |2x + 3| = 3, we need to separate it into two different equations: one with the positive value within the absolute value and another with the negative value within the absolute value.
When the expression inside the absolute value is positive:
2x + 3 = 3
Solve for x:
2x = 3 - 3
2x = 0
x = 0/2
x = 0
When the expression inside the absolute value is negative, we ignore the absolute value symbol and negate the expression:
2x + 3 = -3
Solve for x:
2x = -3 - 3
2x = -6
x = -6/2
x = -3
Therefore, the solutions to the absolute value equation |2x + 3| = 3 are x = 0 and x = -3.
To solve the absolute value equation |2x + 3| = 3, we need to consider two cases based on the positive and negative solutions for the absolute value.
Case 1: 2x + 3 is positive:
In this case, we have 2x + 3 = 3. Subtracting 3 from both sides, we get:
2x = 0
Dividing both sides by 2, we find:
x = 0
Case 2: 2x + 3 is negative:
In this case, we have -(2x + 3) = 3. Applying the distributive property, we get:
-2x - 3 = 3
Adding 3 to both sides, we have:
-2x = 6
Dividing both sides by -2, we get:
x = -3
Therefore, the solutions to the absolute value equation |2x + 3| = 3 are x = 0 and x = -3.