Solve the following absolute value equation.%0D%0A2|4๐ฅ โ 3| + 1 = 9%0D%0Aa) ๐ฅ =โ%0D%0A7%0D%0A4%0D%0A,%0D%0A1%0D%0A4%0D%0Ab) ๐ฅ =%0D%0A7%0D%0A4%0D%0Ac) ๐ฅ = 2, โ%0D%0A1%0D%0A2%0D%0Ad) ๐ฅ =%0D%0A7%0D%0A4%0D%0A, โ%0D%0A1%0D%0A4
To solve the absolute value equation 2|4๐ฅ โ 3| + 1 = 9, we first isolate the absolute value term:
2|4๐ฅ โ 3| = 8
Next, we divide both sides by 2:
|4๐ฅ โ 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: 4๐ฅ โ 3 is positive
4๐ฅ โ 3 = 4
4๐ฅ = 7
๐ฅ = 7/4
Case 2: 4๐ฅ โ 3 is negative
-(4๐ฅ โ 3) = 4
-4๐ฅ + 3 = 4
-4๐ฅ = 1
๐ฅ = -1/4
Therefore, the solutions are ๐ฅ = 7/4 and ๐ฅ = -1/4, which can be written as:
b) ๐ฅ = 7/4
d) ๐ฅ = -1/4