Question

Solve the following absolute value equation.%0D%0A2|4𝑥 − 3| + 1 = 9%0D%0Aa) 𝑥 =−%0D%0A7%0D%0A4%0D%0A,%0D%0A1%0D%0A4%0D%0Ab) 𝑥 =%0D%0A7%0D%0A4%0D%0Ac) 𝑥 = 2, −%0D%0A1%0D%0A2%0D%0Ad) 𝑥 =%0D%0A7%0D%0A4%0D%0A, −%0D%0A1%0D%0A4

Answer 1

To solve the absolute value equation 2|4𝑥 − 3| + 1 = 9, we first isolate the absolute value term:

2|4𝑥 − 3| = 8

Next, we divide both sides by 2:

|4𝑥 − 3| = 4

Now we split the equation into two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 4𝑥 − 3 is positive
4𝑥 − 3 = 4
4𝑥 = 7
𝑥 = 7/4

Case 2: 4𝑥 − 3 is negative
-(4𝑥 − 3) = 4
-4𝑥 + 3 = 4
-4𝑥 = 1
𝑥 = -1/4

Therefore, the solutions are 𝑥 = 7/4 and 𝑥 = -1/4, which can be written as:

b) 𝑥 = 7/4
d) 𝑥 = -1/4