Compare the quantity in Column A with the quantity in Column B.
Column A: 2(x - 3) = 6x
Column B: 3x + 2 = 5x + 6
Could someone help me with the steps to figure this out? I'm having trouble solving these.
Not sure what you mean, either. There is only a single value of x that satisfies each equation. I don't know how you'd turn that fact into columns.
yeah -- I think we got it!
A; 2(x-3) = 6x.
2x - 6 = 6x,
2x - 6x = 6,
-4x = 6,
X = 6/-4 = -6/4 = -3/2.
B: 3x + 2 = 5x + 6.
3x - 5x = 6 - 2,
-2x = 4,
X = -2.
Compare: A/B = (-3/2)/-2 = (-3/2) * (-1/2) = 3/4.
Therefore, A is 3/4 of B.
Ohhh I get it now. I'm homeschooled and my textbook always explains it badly so I was confused, but now I understand. Thanks y'all, I really appreciate the help.
Glad we could help!!
To compare the quantities in Column A and Column B, we need to find the values of x that satisfy both equations. Let's solve each equation step by step.
Column A:
2(x - 3) = 6x
Step 1: Distribute the 2 on the left side of the equation.
2x - 6 = 6x
Step 2: Move all the x terms to one side and constants to the other side.
2x - 6x = 6
-4x = 6
Step 3: Divide both sides of the equation by -4 to isolate x.
x = 6 / -4
x = -3/2 or -1.5
Now let's solve the equation in Column B.
Column B:
3x + 2 = 5x + 6
Step 1: Move all the x terms to one side and constants to the other side.
3x - 5x = 6 - 2
-2x = 4
Step 2: Divide both sides of the equation by -2 to isolate x.
x = 4 / -2
x = -2
Now, we have the values of x for both equations: x = -3/2 or x = -1.5 for Column A, and x = -2 for Column B.
To compare the quantities, we can substitute the values of x back into each equation.
For Column A, when x = -3/2, the equation becomes:
2(-3/2 - 3) = 6(-3/2)
-3 - 6 = -9
-9 = -9
For Column A, when x = -1.5, the equation becomes:
2(-1.5 - 3) = 6(-1.5)
-4.5 = -9
-9 = -9
For Column B, when x = -2, the equation becomes:
3(-2) + 2 = 5(-2) + 6
-6 + 2 = -10 + 6
-4 = -4
Therefore, the quantities in both columns are equal (Column A = Column B) when x = -3/2, -1.5, or -2.