Final answer:
The incomplete equations provided each simplify to a form where we can find a single solution for x by combining like terms and solving for x. Each step involves algebraic simplifications and assuming that each expression is set to be equal to 0. However, without the complete equations or additional information, it is difficult to categorically state the number of solutions.
Step-by-step explanation:
Solving the Given Linear Equations
The equations mentioned in the problem set seem to be incomplete. Assuming they are meant to be equal to something (possibly 0), we'll proceed to solve and categorize them under the assumption that each expression is equal to 0.
a) 2x + 4(x - 1) - 2 + 4x
Distribute the 4 into the parenthses: 2x + 4x - 4 - 2 + 4x.
- Combine like terms: 10x - 6.
- Assuming the equation is set to 0, add 6 to both sides: 10x = 6.
- Divide both sides by 10: x = 0.6.
This equation has one solution: x = 0.6.
b) 25 - * - 15 - (3x + 10) (Note: Assuming the asterisk (*) to be a typo and ignoring it).
Distribute the negative to the parentheses: 25 + 15 - 3x - 10.
- Combine like terms: 30 - 3x.
- Assuming the equation is set to 0, add 3x to both sides: 30 = 3x.
- Divide both sides by 3: x = 10.
This equation has one solution: x = 10.
c) 4x - 2x + 2x + 5(x - x)
Simplify within the parentheses: 5(0).
- 4x - 2x + 2x + 0.
- Combine like terms: 4x.
- Since no constant is involved, assuming the equation is defined, this would simplify to x = 0.
If the equation is to be solved as-is, leading to 4x = 0, the solution would be x = 0. If additional information is given and the equation is set equal to a non-zero term, that would give a different solution.
However, without a complete equation, it is not possible to determine the number of solutions.
In each case, remember to eliminate terms wherever possible to simplify the algebra and carefully check the answer to ensure its reasonability.