Solve these equations algebraically |5𝑥 − 8| = 2

Answer 1

To solve the equation |5𝑥 − 8| = 2 algebraically, we will have two cases:

Case 1: 5𝑥 − 8 is positive (greater than or equal to zero)
We set 5𝑥 − 8 = 2 and solve for 𝑥.
Adding 8 to both sides, we get:
5𝑥 = 10
Dividing both sides by 5, we get:
𝑥 = 2

Case 2: 5𝑥 − 8 is negative (less than zero)
In this case, the absolute value |5𝑥 − 8| is equal to the negation of (5𝑥 − 8).
So, we set -(5𝑥 − 8) = 2 and solve for 𝑥.
Expanding the negative sign, we get:
-5𝑥 + 8 = 2
Subtracting 8 from both sides, we get:
-5𝑥 = -6
Dividing both sides by -5 (remember to flip the inequality when dividing by a negative), we get:
𝑥 = 6/5

Therefore, the solutions to the equation |5𝑥 − 8| = 2 are 𝑥 = 2 and 𝑥 = 6/5.