Solve the equation.
-$$| 5 x - 9 | = | x - 1 |$$

Question

Quizplus · Accepted Answer

To solve the equation $| 5x - 9 | = | x - 1 |$, we consider two cases based on the properties of absolute values:**Case 1:** $5x - 9 = x - 1$Solving for $x$, we subtract $x$ and add $9$ to both sides:$$4x = 8$$$$x = 2$$**Case 2:** $5x - 9 = -(x - 1)$Solving for $x$, we have:$$5x - 9 = -x + 1$$$$6x = 10$$$$x = \frac{10}{6} = \frac{5}{3}$$Thus, the solution set is $\left\{ 2 , \frac { 5 } { 3 } \right\}$.

Solve the Equation ∣5x−9∣=∣x−1∣| 5 x - 9 | = | x - 1 |∣5x−9∣=∣x−1∣

Solve the Equation $| 5 x - 9 | = | x - 1 |$