Question

|a| -3/4 = -5/8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation |a| - 3/4 = -5/8, we can start by isolating |a| on one side of the equation.

First, add 3/4 to both sides:
|a| = -5/8 + 3/4

Now, find a common denominator of 8 for both fractions:
|a| = -5/8 + 6/8

Combine the fractions:
|a| = 1/8

Since the absolute value of a is equal to 1/8, there are two possible solutions for a: a = 1/8 or a = -1/8.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation |a| - 3/4 = -5/8, we need to consider both positive and negative values for "a."

Step 1: Start by isolating the absolute value term on one side.
|a| = -5/8 + 3/4

Step 2: Simplify the right side of the equation by finding a common denominator.
|a| = -5/8 + 6/8

Step 3: Combine the fractions on the right side of the equation.
|a| = 1/8

Step 4: We have two cases to consider for the absolute value.

Case 1: a is positive.
In this case, the absolute value of "a" would be "a" itself.
a = 1/8

Case 2: a is negative.
In this case, the absolute value of "a" would be the negative of "a."
-a = 1/8

Step 5: Solve for "a" in each case.

Case 1:
a = 1/8

Case 2:
Multiply both sides by -1 to isolate "a."
a = -1/8

Therefore, the possible solutions for the equation |a| - 3/4 = -5/8 are a = 1/8 and a = -1/8.

Answer 3

[AI-generated answer — Explain Bot]

To find the value of the variable 'a' in the equation |a| - 3/4 = -5/8, we can follow these steps:

Step 1: Remove the absolute value bars.
When dealing with absolute values, we need to consider both the positive and negative solutions. So, we can rewrite the equation without the absolute value bars as two separate equations: a - 3/4 = -5/8 and -a - 3/4 = -5/8.

Step 2: Solve the first equation for 'a'.
To isolate 'a', we can add 3/4 to both sides of the equation:
a - 3/4 + 3/4 = -5/8 + 3/4
a = -5/8 + 3/4

Step 3: Find a common denominator and add the fractions.
To combine the fractions on the right side, we need to find a common denominator. The least common denominator (LCD) between 8 and 4 is 8. So, we can rewrite the fractions as:

a = -5/8 + (3/4) * (2/2)
a = -5/8 + 6/8
a = 1/8

Step 4: Check the second equation.
Now that we have found a value for 'a', we should check if it satisfies the second equation: -a - 3/4 = -5/8.

Replacing 'a' with the value we found (a = 1/8), the equation becomes:
-(1/8) - 3/4 = -5/8

Simplifying the left side of the equation:
-1/8 - 3/4 = -5/8
-4/8 - 3/4 = -5/8
-7/8 = -5/8

Since the equation is true, the value of 'a' that we found (a = 1/8) is correct.

Therefore, in the equation |a| - 3/4 = -5/8, the value of 'a' that satisfies the equation is a = 1/8.