Which equation has an no solution? 2x+3=2x+7, 4x+22=8x+10, 3x+18=5x+8, 3(4x+8)=4(3x+6).
The equation that has no solution is 3x+18=5x+8.
To determine which equation has no solution, we need to solve each equation and see if we arrive at a contradiction. Let's solve each equation step-by-step:
1) 2x + 3 = 2x + 7
Subtracting 2x from both sides:
2x - 2x + 3 = 2x - 2x + 7
3 = 7
Since the equation simplifies to 3 = 7, which is false, this equation has no solution.
2) 4x + 22 = 8x + 10
Subtracting 4x from both sides:
4x - 4x + 22 = 8x - 4x + 10
22 = 4x + 10
Subtracting 10 from both sides:
22 - 10 = 4x + 10 - 10
12 = 4x
Dividing both sides by 4:
12 / 4 = 4x / 4
3 = x
This equation has a solution, with x = 3.
3) 3x + 18 = 5x + 8
Subtracting 3x from both sides:
3x - 3x + 18 = 5x - 3x + 8
18 = 2x + 8
Subtracting 8 from both sides:
18 - 8 = 2x + 8 - 8
10 = 2x
Dividing both sides by 2:
10 / 2 = 2x / 2
5 = x
This equation has a solution, with x = 5.
4) 3(4x + 8) = 4(3x + 6)
Distributing on both sides:
3 * 4x + 3 * 8 = 4 * 3x + 4 * 6
12x + 24 = 12x + 24
Simplifying both sides, we see that all terms cancel out and we are left with 24 = 24.
Since the equation simplifies to a true statement, 24 = 24, this equation has infinitely many solutions.
In conclusion, the equation 2x + 3 = 2x + 7 has no solution.
To determine which equation has no solution, we need to solve each equation and see if we arrive at a contradiction or an impossible condition. Let's examine each equation step by step:
1) 2x + 3 = 2x + 7
Subtracting 2x from both sides, we get:
3 = 7
This equation simplifies to a contradiction: 3 is not equal to 7. Therefore, this equation has no solution.
2) 4x + 22 = 8x + 10
Subtracting 4x from both sides, we get:
22 = 4x + 10
Subtracting 10 from both sides, we get:
12 = 4x
Dividing both sides by 4, we get:
3 = x
This equation simplifies to a single solution: x = 3. Therefore, this equation does have a solution.
3) 3x + 18 = 5x + 8
Subtracting 3x from both sides, we get:
18 = 2x + 8
Subtracting 8 from both sides, we get:
10 = 2x
Dividing both sides by 2, we get:
5 = x
This equation simplifies to a single solution: x = 5. Therefore, this equation does have a solution.
4) 3(4x + 8) = 4(3x + 6)
Distributing on both sides, we get:
12x + 24 = 12x + 24
Subtracting 12x from both sides, we get:
24 = 24
This equation simplifies to an identity: 24 is equal to 24. Therefore, this equation has infinite solutions.
In summary, the equation that has no solution is 2x + 3 = 2x + 7.