Question Solve for all values of \( x \) in simplest form. \[ 4=|3 x+2| \] Answer Attempt 1 out of 10

To solve the equation \( 4 = |3x + 2| \), we need to consider the definition of absolute value. This means we can split the equation into two cases: 1. \( 3x + 2 = 4 \) 2. \( 3x + 2 = -4 \) For the first case, solving \( 3x + 2 = 4 \) gives us: \[ 3x = 4 - 2 \] \[ 3x = 2 \quad \Rightarrow \quad x = \frac{2}{3} \] For the second case, solving \( 3x + 2 = -4 \) gives us: \[ 3x = -4 - 2 \] \[ 3x = -6 \quad \Rightarrow \quad x = -2 \] Thus, the solutions for \( x \) are \( \frac{2}{3} \) and \( -2 \). Now, let's check our work: Plugging \( x = \frac{2}{3} \) into the original equation results in \( 4 = |4| \), and \( x = -2 \) results in \( 4 = | -4 | \). Both hold true! In conclusion, the values of \( x \) that satisfy the equation are \( x = \frac{2}{3} \) and \( x = -2 \). 🎉