Exercise \( \mathbf{6} \) (Revision) Solve the following equations. \( \begin{array}{ll}\text { (1) } 4 x=3 x+5 & \text { (2) } 7 m=8+5 m \\ \text { (3) } 2 a=9-a & \text { (4) } \frac{1}{4} d=3 \\ \text { (5) } 5 y+6=21 & \text { (6) } 2 n-3=6\end{array} \)

Solve the equation by following steps: - step0: Solve for \(a\): \(2a=9-a\) - step1: Move the variable to the left side: \(2a+a=9\) - step2: Add the terms: \(3a=9\) - step3: Divide both sides: \(\frac{3a}{3}=\frac{9}{3}\) - step4: Divide the numbers: \(a=3\) Solve the equation \( 5y+6=21 \). Solve the equation by following steps: - step0: Solve for \(y\): \(5y+6=21\) - step1: Move the constant to the right side: \(5y=21-6\) - step2: Subtract the numbers: \(5y=15\) - step3: Divide both sides: \(\frac{5y}{5}=\frac{15}{5}\) - step4: Divide the numbers: \(y=3\) Solve the equation \( 4x=3x+5 \). Solve the equation by following steps: - step0: Solve for \(x\): \(4x=3x+5\) - step1: Move the variable to the left side: \(4x-3x=5\) - step2: Subtract the terms: \(x=5\) Solve the equation \( 2n-3=6 \). Solve the equation by following steps: - step0: Solve for \(n\): \(2n-3=6\) - step1: Move the constant to the right side: \(2n=6+3\) - step2: Add the numbers: \(2n=9\) - step3: Divide both sides: \(\frac{2n}{2}=\frac{9}{2}\) - step4: Divide the numbers: \(n=\frac{9}{2}\) Solve the equation \( \frac{1}{4}d=3 \). Solve the equation by following steps: - step0: Solve for \(d\): \(\frac{1}{4}d=3\) - step1: Multiply by the reciprocal: \(\frac{1}{4}d\times 4=3\times 4\) - step2: Multiply: \(d=12\) Solve the equation \( 7m=8+5m \). Solve the equation by following steps: - step0: Solve for \(m\): \(7m=8+5m\) - step1: Move the variable to the left side: \(7m-5m=8\) - step2: Subtract the terms: \(2m=8\) - step3: Divide both sides: \(\frac{2m}{2}=\frac{8}{2}\) - step4: Divide the numbers: \(m=4\) Here are the solutions to the equations provided: 1. **Equation:** \( 4x = 3x + 5 \) **Solution:** \[ x = 5 \] 2. **Equation:** \( 7m = 8 + 5m \) **Solution:** \[ m = 4 \] 3. **Equation:** \( 2a = 9 - a \) **Solution:** \[ a = 3 \] 4. **Equation:** \( \frac{1}{4}d = 3 \) **Solution:** \[ d = 12 \] 5. **Equation:** \( 5y + 6 = 21 \) **Solution:** \[ y = 3 \] 6. **Equation:** \( 2n - 3 = 6 \) **Solution:** \[ n = \frac{9}{2} \quad \text{or} \quad n = 4.5 \] If you have any further questions or need additional assistance, feel free to ask!