(2) In each of the following expren of other variables; write \( z \) in terms of \( 2.1 x=\sqrt{z+y} \) \( 2.2 x=\frac{\text { abcz }}{3} \) \( 2.3 a=b-3 z \) \( 2.4 y=\frac{\sqrt{z}}{5} \) \( 2.6 y=\frac{3-2 z}{x+z}-1 \) \( 2.5 x=\frac{3 z+m}{2}-1 \)

Sure, let's solve each equation for \( z \) in terms of the other variables. --- ### **2.1** \( x = \sqrt{z + y} \) **Solution:** 1. Square both sides to eliminate the square root: \[ x^2 = z + y \] 2. Solve for \( z \): \[ z = x^2 - y \] **Answer:** \[ z = x^2 - y \] --- ### **2.2** \( x = \frac{\text{abcz}}{3} \) **Solution:** 1. Multiply both sides by 3 to isolate \( \text{abcz} \): \[ 3x = \text{abcz} \] 2. Divide both sides by \( \text{abc} \) (assuming \( \text{abc} \neq 0 \)): \[ z = \frac{3x}{\text{abc}} \] **Answer:** \[ z = \frac{3x}{\text{abc}} \] --- ### **2.3** \( a = b - 3z \) **Solution:** 1. Subtract \( b \) from both sides: \[ a - b = -3z \] 2. Divide both sides by \( -3 \): \[ z = \frac{b - a}{3} \] **Answer:** \[ z = \frac{b - a}{3} \] --- ### **2.4** \( y = \frac{\sqrt{z}}{5} \) **Solution:** 1. Multiply both sides by 5: \[ 5y = \sqrt{z} \] 2. Square both sides to eliminate the square root: \[ 25y^2 = z \] **Answer:** \[ z = 25y^2 \] --- ### **2.5** \( x = \frac{3z + m}{2} - 1 \) **Solution:** 1. Add 1 to both sides: \[ x + 1 = \frac{3z + m}{2} \] 2. Multiply both sides by 2: \[ 2(x + 1) = 3z + m \] 3. Subtract \( m \) from both sides: \[ 2x + 2 - m = 3z \] 4. Divide both sides by 3: \[ z = \frac{2x + 2 - m}{3} \] **Answer:** \[ z = \frac{2x + 2 - m}{3} \] --- ### **2.6** \( y = \frac{3 - 2z}{x + z} - 1 \) **Solution:** 1. Add 1 to both sides: \[ y + 1 = \frac{3 - 2z}{x + z} \] 2. Multiply both sides by \( x + z \): \[ (y + 1)(x + z) = 3 - 2z \] 3. Expand the left side: \[ yx + y z + x + z = 3 - 2z \] 4. Collect like terms involving \( z \): \[ z(y + 1) + 2z = 3 - yx - x \] 5. Factor out \( z \): \[ z(y + 3) = 3 - x(y + 1) \] 6. Divide both sides by \( y + 3 \) (assuming \( y + 3 \neq 0 \)): \[ z = \frac{3 - x(y + 1)}{y + 3} \] **Answer:** \[ z = \frac{3 - x(y + 1)}{y + 3} \] --- Feel free to reach out if you have any further questions!