(A) Simply the following equations: \( \begin{array}{ll}\text { i. } 2(x+5)=18 & \text { (4 Marks) } \\ \text { ii. } \quad \underline{22-3 x}=2 x & \text { ( } 4 \text { Marks) }\end{array} \)

Solve the equation by following steps: - step0: Solve for \(x\): \(2\left(x+5\right)=18\) - step1: Divide both sides: \(\frac{2\left(x+5\right)}{2}=\frac{18}{2}\) - step2: Divide the numbers: \(x+5=9\) - step3: Move the constant to the right side: \(x=9-5\) - step4: Subtract the numbers: \(x=4\) Solve the equation \( 22-3 x=2 x \). Solve the equation by following steps: - step0: Solve for \(x\): \(22-3x=2x\) - step1: Move the variable to the left side: \(22-3x-2x=0\) - step2: Subtract the terms: \(22-5x=0\) - step3: Move the constant to the right side: \(-5x=0-22\) - step4: Remove 0: \(-5x=-22\) - step5: Change the signs: \(5x=22\) - step6: Divide both sides: \(\frac{5x}{5}=\frac{22}{5}\) - step7: Divide the numbers: \(x=\frac{22}{5}\) Let's simplify the given equations step by step. ### Equation (i): \[ 2(x+5) = 18 \] 1. **Distribute the 2**: \[ 2x + 10 = 18 \] 2. **Subtract 10 from both sides**: \[ 2x = 18 - 10 \] \[ 2x = 8 \] 3. **Divide both sides by 2**: \[ x = \frac{8}{2} \] \[ x = 4 \] ### Equation (ii): \[ 22 - 3x = 2x \] 1. **Add \(3x\) to both sides**: \[ 22 = 2x + 3x \] \[ 22 = 5x \] 2. **Divide both sides by 5**: \[ x = \frac{22}{5} \] \[ x = 4.4 \] ### Summary of Results: - For equation (i), the solution is \( x = 4 \). - For equation (ii), the solution is \( x = \frac{22}{5} \) or \( x = 4.4 \).