Which equation has no solution? 2x+3=2x+7, 4x+22=8x+10, 5x+5=5x+4, 3x+18=5x+8, 3(4x+8)=4(3x+6).
The equation that has no solution is the equation where the variable cancels out and results in inequality or contradiction.
In this case, the equation 3x+18=5x+8 has no solution.
To determine which equation has no solution, we need to solve each equation and see if we can find a solution.
1) 2x + 3 = 2x + 7
Subtracting 2x from both sides:
3 = 7
This is not true, so there is no solution for this equation.
2) 4x + 22 = 8x + 10
Subtracting 4x from both sides:
22 = 4x + 10
Subtracting 10 from both sides:
12 = 4x
Dividing both sides by 4:
3 = x
This equation has a solution: x = 3.
3) 5x + 5 = 5x + 4
Subtracting 5x from both sides:
5 = 4
This is not true, so there is no solution for this equation.
4) 3x + 18 = 5x + 8
Subtracting 3x from both sides:
18 = 2x + 8
Subtracting 8 from both sides:
10 = 2x
Dividing both sides by 2:
5 = x
This equation has a solution: x = 5.
5) 3(4x + 8) = 4(3x + 6)
Distributing on both sides:
12x + 24 = 12x + 24
Subtracting 12x from both sides:
24 = 24
This equation is true for any value of x. Therefore, it has infinitely many solutions.
In summary, the equation that has no solution is: 2x + 3 = 2x + 7.
To determine which equation has no solution, we need to solve each equation and check if the variable cancels out and leads to a false statement. Let's solve each equation step by step:
1) 2x+3=2x+7:
To solve this equation, we can subtract 2x from both sides:
2x - 2x + 3 = 2x - 2x + 7
0 + 3 = 0 + 7
3 = 7
We have reached a false statement (3 ≠ 7), which means that this equation has no solution.
2) 4x+22=8x+10:
Let's subtract 4x from both sides:
4x - 4x + 22 = 8x - 4x + 10
0 + 22 = 4x + 10
22 = 4x + 10
Next, we can subtract 10 from both sides:
22 - 10 = 4x + 10 - 10
12 = 4x
Finally, divide both sides by 4 to isolate x:
12/4 = 4x/4
3 = x
We have found a solution for x, so this equation does have a solution.
3) 5x+5=5x+4:
Subtracting 5x from both sides, we get:
5x - 5x + 5 = 5x - 5x + 4
0 + 5 = 0 + 4
5 = 4
Again, this equation has led to a false statement (5 ≠ 4), so it has no solution.
4) 3x+18=5x+8:
Let's begin by subtracting 3x from both sides:
3x - 3x + 18 = 5x - 3x + 8
0 + 18 = 2x + 8
18 = 2x + 8
Next, subtract 8 from both sides:
18 - 8 = 2x + 8 - 8
10 = 2x
Finally, divide both sides by 2:
10/2 = 2x/2
5 = x
So, this equation does have a solution.
5) 3(4x+8)=4(3x+6):
Let's distribute the multiplication on both sides:
12x + 24 = 12x + 24
We can see that the equation is already balanced. The variable x cancels out, and we are left with a true statement (24 = 24).
Since the variable cancels out and the equation is true, it means that this equation has infinitely many solutions.
In summary, the equations that have no solution are:
1) 2x+3=2x+7
3) 5x+5=5x+4