Question

1. solve the absolute value function. (4pts)

6|1 - 5x| - 9 = 57

Explanation:

Step1: Isolate the absolute value term

Add 9 to both sides of the equation:
$6|1 - 5x| - 9 + 9 = 57 + 9$
Simplify: $6|1 - 5x| = 66$

Step2: Divide by the coefficient of the absolute value

Divide both sides by 6:
$\frac{6|1 - 5x|}{6} = \frac{66}{6}$
Simplify: $|1 - 5x| = 11$

Step3: Solve the two cases for absolute value

Case 1: $1 - 5x = 11$
Subtract 1: $-5x = 10$
Divide by -5: $x = -2$

Case 2: $1 - 5x = -11$
Subtract 1: $-5x = -12$
Divide by -5: $x = \frac{12}{5} = 2.4$

Answer:

$x = -2$ or $x = \frac{12}{5}$ (or $x = 2.4$)