Solve the equation. Then determine whether the equation is ar equation. \( 4 x+27=9(x+3)-5 x \) What is the solution? Select the correct choice below and, if ne

Let's solve the equation step by step and determine its nature. **Given Equation:** \[ 4x + 27 = 9(x + 3) - 5x \] **Step 1: Expand and Simplify Both Sides** 1. Expand the right-hand side (RHS): \[ 9(x + 3) = 9x + 27 \] 2. Substitute back into the equation: \[ 4x + 27 = 9x + 27 - 5x \] 3. Combine like terms on the RHS: \[ 9x - 5x = 4x \] 4. Now, the equation is: \[ 4x + 27 = 4x + 27 \] **Step 2: Solve for \( x \)** Subtract \( 4x \) from both sides: \[ 4x + 27 - 4x = 4x + 27 - 4x \] \[ 27 = 27 \] **Analysis:** The equation simplifies to a true statement \( 27 = 27 \), which means that the original equation holds true for **all real numbers** \( x \). There is no unique solution; instead, there are **infinitely many solutions**. **Conclusion:** - **Solution:** The equation is true for all real numbers \( x \) (infinitely many solutions). - **Type of Equation:** It is an **identity** (a statement that is always true). **Answer Summary:** All real numbers satisfy the equation. Since it is always true, the equation has infinitely many solutions.