Questions: 4x-1 / -2 = -16

Transcript text: $\frac{|4 x-1|}{-2}=-16$

Solution

Solution Steps

To solve the equation $\frac{|4x - 1|}{-2} = -16$, we can follow these steps:

Multiply both sides of the equation by $-2$ to eliminate the fraction.
Solve the resulting absolute value equation.
Consider both the positive and negative scenarios of the absolute value to find the possible values of $x$.

Step 1: Understand the Problem

We are given the equation: \[ \frac{|4x - 1|}{-2} = -16 \] We need to solve for $ x $.

Step 2: Isolate the Absolute Value Expression

First, we need to isolate the absolute value expression. Multiply both sides of the equation by $-2$ to get rid of the denominator: \[ |4x - 1| = (-16) \times (-2) \] \[ |4x - 1| = 32 \]

Step 3: Solve the Absolute Value Equation

The absolute value equation $ |4x - 1| = 32 $ can be split into two separate equations: \[ 4x - 1 = 32 \quad \text{or} \quad 4x - 1 = -32 \]

Step 4: Solve Each Equation Separately

Equation 1: $ 4x - 1 = 32 $

Add 1 to both sides: \[ 4x = 33 \] Divide by 4: \[ x = \frac{33}{4} \]

Equation 2: $ 4x - 1 = -32 $

Add 1 to both sides: \[ 4x = -31 \] Divide by 4: \[ x = \frac{-31}{4} \]