Answer: A and D
Explanation:
**REFERENCE**
Variable term: An x term, or a number with an x beside it, like 5x, 3x, 9x, etc.
Constant: A number with no letter beside it, like 5, 3, 10, and 1.
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There are 2 ways to answer this. One is to solve all the equations, but another is to remember 3 simple rules.
1. For an equation to have one solution, they must have different variable terms and different constant terms.
- Example: 2x+12= 3x+15. The variable terms, 2x and 3x are ddifferent, and 12 and 15, the constants, are different as well.
2. For an equation to have no solutions, they must have the same variables on both sides, but different constants.
- Example: 2x+12=2x+9. The variables, 2x, are the same, but the constants, 12 and 9, are obviously different.
3. For an equation to have infinite solutions, both the variable and the constant terms must be the same on both sides.
- An example of an equation with infinite solutions is 2x+12=2x+12. The variable terms, 2x, are the same, and the constant term, 12, is also the same on both sides,
That being said, let's look at the 4 answer choices and determine how many solutions they have.
A. -5x+12=-12x-12
Rearranged for context: 12-5x= -12-12x
Variable terms: -5x and -12x. The variable terms are different.
Constant terms: 12 and -12. The constant terms are different
In option A, the variable and the constant terms are different. therefore it has 1 solution. A is correct.
B. -5x+12=5x+12
Rearranged for context: 12-5x=12+5x
Variable terms: -5x and 5x. They are different
Constant terms: 12 and 12. They are the same.
In option B, the variable terms are different but the constant terms are the same. This one is very confusing but since they don't have BOTH different variables and constants, I'll just assume that it doesn't have 1 solution.
C. -5x+12=-5x-12
Variable terms: -5x and -5x. SAME VARIABLES
Constant terms: 12 and -12. DIFFERENT CONSTANTS
No solutions
D. -5x+12=5x-5
Variables: -5x and 5x
Constants: 12 and -5
BOTH DIFFERENT
1 SOLUTION
D is correct.
hope this helps!! :D