Plug more than one point into the original equation and check to show that the equations can have more than one solution. Explain your work.
3(4x+8)=4(3x+6)
To check if an equation can have more than one solution, we need to verify if different values for the variable yield true statements when plugged into the equation.
The original equation is:
3(4x+8)=4(3x+6)
Let's choose two different values of x and see if the equation holds true:
For x=0:
3(4(0)+8)=4(3(0)+6)
3(8)=4(6)
24=24
For x=1:
3(4(1)+8)=4(3(1)+6)
3(12)=4(9)
36=36
In both cases, the equation remains true. Therefore, the equation has more than one solution.
To show that the equation 3(4x+8)=4(3x+6) can have more than one solution, we need to plug in more than one point into the equation and verify if the equation holds true for each point.
Let's choose two arbitrary points, A and B, and plug them into the equation:
Point A: Let x = 1
Substituting x=1 into the equation, we have:
3(4(1)+8) = 4(3(1)+6)
3(4+8) = 4(3+6)
3(12) = 4(9)
36 = 36
The equation holds true for point A.
Point B: Let x = 2
Substituting x=2 into the equation, we have:
3(4(2)+8) = 4(3(2)+6)
3(8+8) = 4(6+6)
3(16) = 4(12)
48 = 48
The equation also holds true for point B.
Since the equation holds true for both point A and point B, we can conclude that the equation can have more than one solution. In this case, the equation has infinitely many solutions since any value of x that satisfies the equation would be a valid solution.
To check if the equation 3(4x+8) = 4(3x+6) has more than one solution, we need to plug in more than one point into the equation and see if it satisfies the equation.
Let's choose two different values for x, and substitute them into the equation to see if both values give us a true statement. Let's use x = 1 and x = -2.
When x = 1:
3(4(1) + 8) = 4(3(1) + 6)
3(4 + 8) = 4(3 + 6)
3(12) = 4(9)
36 = 36
When x = -2:
3(4(-2) + 8) = 4(3(-2) + 6)
3(-8 + 8) = 4(-6 + 6)
3(0) = 4(0)
0 = 0
As we can see, both values of x satisfy the equation, resulting in a true statement. This means that the equation 3(4x+8) = 4(3x+6) has more than one solution.