Answer : x = -3/4 and x = -17/4
Explanation:
To solve the equation 8 + 3 ∣ 4x + 10 ∣ = 29, we need to isolate the absolute value expression and solve for x.
1. Subtract 8 from both sides of the equation:
3 ∣ 4x + 10 ∣ = 29 - 8
3 ∣ 4x + 10 ∣ = 21
2. Divide both sides of the equation by 3:
∣ 4x + 10 ∣ = 21/3
∣ 4x + 10 ∣ = 7
3. Now we have two cases to consider:
Case 1: 4x + 10 ≥ 0
Case 2: 4x + 10 < 0
For Case 1, when 4x + 10 ≥ 0:
We can remove the absolute value sign:
4x + 10 = 7
Subtract 10 from both sides:
4x = 7 - 10
4x = -3
Divide both sides by 4:
x = -3/4
For Case 2, when 4x + 10 < 0:
We can remove the absolute value sign by changing the sign:
-(4x + 10) = 7
Distribute the negative sign:
-4x - 10 = 7
Add 10 to both sides:
-4x = 7 + 10
-4x = 17
Divide both sides by -4 (remember to change the sign when dividing by a negative number):
x = 17/(-4)
x = -17/4
Therefore, the two solutions for x in simplest form are:
x = -3/4 and x = -17/4