simplify and explain
To find out whether the answer to the equation is one-eighth or negative one-eighth, we will need to solve the equation step by step:
1. Start with the given equation: |a| - 3/4 = -5/8.
2. Add 3/4 to both sides of the equation: |a| = -5/8 + 3/4.
3. Simplify the right side of the equation: -5/8 + 3/4 = -5/8 + 6/8 = 1/8.
4. Now we have |a| = 1/8. To solve for a, we need to consider both the positive and negative case for the absolute value.
5. Positive case: a = 1/8. This means that if a equals 1/8, the equation holds true.
6. Negative case: a = -1/8. If a equals -1/8, the equation still holds true.
Therefore, the answer to the equation |a| - 3/4 = -5/8 can be either one-eighth (1/8) or negative one-eighth (-1/8).
This explanation breaks down the steps taken to solve the equation |a| - 3/4 = -5/8.
1. The given equation is |a| - 3/4 = -5/8.
2. To isolate the absolute value term, add 3/4 to both sides of the equation.
3. By simplifying the right side of the equation, -5/8 + 3/4 equals -5/8 + 6/8, which simplifies further to 1/8.
4. This results in the equation |a| = 1/8.
5. Since the absolute value of a can be either positive or negative, consider both cases.
6. In the positive case, a = 1/8, meaning that if a is equal to 1/8, the equation is true.
7. In the negative case, a = -1/8, indicating that if a is equal to -1/8, the equation is still true.
8. Therefore, the possible answers to the equation |a| - 3/4 = -5/8 are one-eighth (1/8) or negative one-eighth (-1/8).