Question

If w = 3z+2/2z+1 , show that z = -w+2/2w-3 . Hence solve the equation (3z+2)³ = -27(2z+1)³ by first expressing it in terms of w.

Answer 1

To show that z = -w+2/2w-3, we can start with the given equation w = 3z+2/2z+1 and manipulate it step-by-step. After deriving the expression for z, we can substitute it back into the equation to solve for w.

Step-by-step explanation:

To show that z = -w+2/2w-3, we need to start with the given equation w = 3z+2/2z+1 and manipulate it to solve for z. Here's the step-by-step process:

1. Multiply both sides of the equation by (2z+1) to eliminate the denominator: (2z+1)w = 3z+2
2. Distribute w on the left side: 2zw + w = 3z + 2
3. Move all the z terms to one side of the equation and all the w terms to the other side: 3z - 2zw = w - 2
4. Factor out z on the left side: z(3 - 2w) = w - 2
5. Divide both sides by (3 - 2w) to isolate z: z = (w - 2)/(3 - 2w)
6. Now, substitute -w+2/2w-3 into the equation for z: z = (-w+2)/(2w-3)

To solve the equation (3z+2)³ = -27(2z+1)³ in terms of w, we can substitute z = (-w+2)/(2w-3) into the equation. This will give us an equation solely in terms of w, which we can solve. Good luck!