My math question ask is 1/3(x-9) = 2x+7 greater than or less than 4/3(x+4)= -4x.
The problem (1) answer = 6. Problem (2) answer = -1. Therefore problem (2) is less than problem (1). Are the answer to the equations correct.
Sincerely
The question makes no sense.
Equations do not have a numerical value.
They should have asked
Is the solution to 1/3(x-9) = 2x+7 greater than or less than the solution to 4/3(x+4) = -4x
To say that one equation is greater than another equation makes absolutely no sense.
As to the actual answers to your equations ...
1.
1/3(x-9) = 2x+7
x-9 = 6x + 21
-5x = 30
x = -6 , you had +6
2.
4/3(x+4) = -4x
4(x+4) = -12x
divide both sides by 4
x+4 = -3x
4x = -4
x = -1 , yeah, you had that one right
To determine if the answer to the equations is correct, we need to solve both equations and compare the results.
Let's start by solving the first equation: 1/3(x-9) = 2x+7.
1. Distribute the 1/3 to the terms inside the parentheses: (1/3)x - 3 = 2x + 7.
2. Move the variables to one side and the constants to the other side: (1/3)x - 2x = 7 + 3.
3. Combine like terms: (-5/3)x = 10.
4. Divide both sides by the coefficient of x (-5/3) to isolate x: x = 10 / (-5/3).
5. Simplify the right side: x = -6.
So the solution to the first equation is x = -6.
Now let's solve the second equation: 4/3(x+4) = -4x.
1. Distribute the 4/3 to the terms inside the parentheses: (4/3)x + 16/3 = -4x.
2. Move the variables to one side and the constants to the other side: (4/3)x + 4x = -16/3.
3. Combine like terms: (4/3 + 12/3)x = -16/3.
4. Simplify the left side: (16/3)x = -16/3.
5. Divide both sides by the coefficient of x (16/3) to isolate x: x = -16/3 / (16/3).
6. Simplify the right side: x = -1.
So the solution to the second equation is x = -1.
Now, let's compare the solutions. The first solution is x = -6, and the second solution is x = -1. From these results, we can see that -1 is greater than -6. Therefore, the answer to the second equation, x = -1, is indeed less than the answer to the first equation, x = -6.
So, the statement "Problem (2) is less than Problem (1)" is correct based on the given solutions.