Questions: Solve the equation 4x+2=11

Transcript text: Solve the equation $|4 x+2|=11$

Solution

Step 1: Set Up the Absolute Value Equation

We start with the equation involving the absolute value: $|4x + 2| = 11$

Step 2: Split into Two Linear Equations

To solve the absolute value equation, we split it into two separate linear equations:

Step 3: Solve Each Linear Equation

Solving

4x + 2 = 11

$4x + 2 = 11$ Subtract 2 from both sides: $4x = 9$ Divide by 4: $x = \frac{9}{4}$

Solving

4x + 2 = -11

$4x + 2 = -11$ Subtract 2 from both sides: $4x = -13$ Divide by 4: $x = -\frac{13}{4}$

$\boxed{x = \frac{9}{4}, -\frac{13}{4}}$

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