Sort the equations between Infinite solutions, no solutions, or one solution
8x+10=8x+10
3x+5=3x-6
6x+8≥2x-4
4x+8>4x+10
4x-4+2x=6x-4
1. 8x+10=8x+10 - Infinite solutions
2. 3x+5=3x-6 - No solutions
3. 6x+8≥2x-4 - One solution
4. 4x+8>4x+10 - No solutions
5. 4x-4+2x=6x-4 - One solution
Let's analyze each equation step by step:
1. 8x + 10 = 8x + 10
- Subtracting 8x from both sides gives us: 10 = 10
- Since the equation is true for any value of x, it has infinite solutions.
2. 3x + 5 = 3x - 6
- Subtracting 3x from both sides gives us: 5 = -6
- This equation is not true, regardless of the value of x. It has no solutions.
3. 6x + 8 ≥ 2x - 4
- Subtracting 2x from both sides gives us: 4x + 8 ≥ -4
- Then, subtracting 8 from both sides gives us: 4x ≥ -12
- Finally, dividing both sides by 4 gives us: x ≥ -3
- This equation has infinite solutions because any value equal to or greater than -3 satisfies the inequality.
4. 4x + 8 > 4x + 10
- Subtracting 4x from both sides gives us: 8 > 10
- This equation is not true, regardless of the value of x. It has no solutions.
5. 4x - 4 + 2x = 6x - 4
- Combining like terms gives us: 6x - 4 = 6x - 4
- When we subtract 6x from both sides, we get: -4 = -4
- Similar to the first equation, this equation is true for any value of x, so it has infinite solutions.
In summary:
- Equation 1 has infinite solutions.
- Equation 2 has no solutions.
- Equation 3 has infinite solutions.
- Equation 4 has no solutions.
- Equation 5 has infinite solutions.