Question

Solve the following equations for x (find all solutions or state that none exist). (i) (9⊗x)⨁4=1 (ii) 2⊗x=4 (iii) 2⊗x=3.

Answer 1

Without the context for the operations denoted by ⊗ and ⊕, it's not possible to provide an accurate solution for the equations. However, treating these symbols as standard multiplication and addition respectively, we can solve them using basic algebraic methods.

Step-by-step explanation:

Solving the Given Equations for x To solve the following equations for x (find all solutions or state that none exist), we need to understand the operations represented by ⊗ and ⊕. Assuming they stand for multiplication (⊗) and addition (⊕), the equations provided would be interpreted and solved as follows:

1. (9⊗x)⊕4=1
2. 2⊗x=4
3. 2⊗x=3

However, without context for the operations ⊗ and ⊕, it's not possible to give an exact solution. To solve equations like these, we generally:

• Identify the unknowns.
• Determine the known values.
• Choose an equation and plug in the known values.
• Solve for the unknown.
• Check the math.

In cases where the notation is standard algebra, the equations could be solved as follows:

1. For 9x + 4 = 1, we would subtract 4 from both sides and then divide by 9.
2. For 2x = 4, we would divide both sides by 2.
3. For 2x = 3, again divide both sides by 2.

Nevertheless, without clarification on the operations, we cannot provide an accurate solution. If ⊗ and ⊕ are indeed standard multiplication and addition respectively, the solutions would be: x = -1/3 for equation (i), x = 2 for equation (ii), and x = 3/2 for equation (iii).