Which equation has an infinite 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 an infinite solution is: 5x+5=5x+4.
The equation that has an infinite solution is the equation: 3x + 18 = 5x + 8.
To solve this equation, we start by simplifying both sides:
3x + 18 = 5x + 8
First, we can subtract 3x from both sides to eliminate the variable on the left side:
18 = 2x + 8
Next, we can subtract 8 from both sides:
10 = 2x
Now, we divide both sides by 2 to solve for x:
10/2 = x
5 = x
So, the equation 3x + 18 = 5x + 8 has an infinite solution because any value of x, such as x = 5, will satisfy the equation.
To determine which equation has an infinite solution, we need to solve each equation and see if the solution satisfies the given equation.
1) 2x + 3 = 2x + 7
Subtracting 2x from both sides, we get:
3 = 7
Since 3 does not equal 7, 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 has a unique solution: x = 3.
3) 5x + 5 = 5x + 4
Notice that the x terms cancel out when subtracting 5x from both sides:
5 = 4
Since 5 does not equal 4, this equation has no solution.
4) 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 has a unique solution: x = 5.
5) 3(4x + 8) = 4(3x + 6)
Distributing on the left side, we get:
12x + 24 = 12x + 24
Subtracting 12x from both sides, we get:
24 = 24
Since 24 equals 24, this equation has an infinite number of solutions.
Thus, the equation "3(4x+8) = 4(3x+6)" has an infinite solution.