Answer: x = 143/56 and x = -185/56.
Explanation:
Case 1: (2x + 3/4) is positive
2x + 3/4 = 5 6/7
First, convert the mixed fraction 5 6/7 to an improper fraction:
5 6/7 = 41/7
Now solve for x:
2x + 3/4 = 41/7
Subtract 3/4 from both sides:
2x = 41/7 - 3/4
Find a common denominator for 7 and 4, which is 28:
2x = (4 * 41)/(4 * 7) - (3 * 7)/(3 * 4)
2x = 164/28 - 21/28
2x = (164 - 21)/28
2x = 143/28
Divide both sides by 2:
x = 143/56
Case 2: (2x + 3/4) is negative
(2x + 3/4) = 5 6/7
Again, convert the mixed fraction to an improper fraction:
5 6/7 = 41/7
Now solve for x:
(2x + 3/4) = 41/7
Distribute the negative sign:
-2x - 3/4 = 41/7
Add 3/4 to both sides:
-2x = 41/7 + 3/4
Find a common denominator for 7 and 4, which is 28:
-2x = (4 * 41)/(4 * 7) + (3 * 7)/(3 * 4)
-2x = 164/28 + 21/28
-2x = (164 + 21)/28
-2x = 185/28
Divide both sides by -2:
x = -185/56
So, the solutions for the equation |2x + 3/4| = 5 6/7 are x = 143/56 and x = -185/56.