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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