Which of the following are equivalent to the ratio left-parenthesis 2 x minus 6 right-parenthesis colon left-parenthesis 6 x minus 4 right-parenthesis?
(1 point)
Responses
negative 2 colon 1
Image with alt text: negative 2 colon 1
X minus 3 colon 3 x minus 2
Image with alt text: X minus 3 colon 3 x minus 2
3 x colon x
Image with alt text: 3 x colon x
Left-parenthesis 4 x minus 12 right-parenthesis colon left-parenthesis 12 x minus 8 right-parenthesis
Image with alt text: Left-parenthesis 4 x minus 12 right-parenthesis colon left-parenthesis 12 x minus 8 right-parenthesis
x minus 1 colon x minus 2
Image with alt text: x minus 1 colon x minus 2
pick 3 of the ones above.
The three options that are equivalent to the ratio (2x - 6) : (6x - 4) are:
1. Negative 2 : 1
2. X minus 3 : 3x minus 2
3. Left-parenthesis 4x minus 12 right-parenthesis : left-parenthesis 12x minus 8 right-parenthesis
To determine which option is equivalent to the ratio left-parenthesis 2 x minus 6 right-parenthesis colon left-parenthesis 6 x minus 4 right-parenthesis, we can simplify each option and compare them.
1. Option: negative 2 colon 1
To simplify, we can divide both terms by the greatest common factor, which is 1. The ratio becomes negative 2 colon 1, which means -2:1.
2. Option: X minus 3 colon 3 x minus 2
To simplify, we can factor out a common factor from both terms. The ratio becomes (x - 3) colon (3x - 2).
3. Option: 3 x colon x
To simplify, we can divide both terms by the greatest common factor, which is x. The ratio becomes 3:1.
4. Option: Left-parenthesis 4 x minus 12 right-parenthesis colon left-parenthesis 12 x minus 8 right-parenthesis
To simplify, we can factor out a common factor from both terms. The ratio becomes (4x - 12) colon (12x - 8).
5. Option: x minus 1 colon x minus 2
This option is already in simplified form.
Now, we can compare the simplified ratios:
- Option 1: -2:1
- Option 2: (x - 3) colon (3x - 2)
- Option 3: 3:1
- Option 4: (4x - 12) colon (12x - 8)
- Option 5: x - 1 colon x - 2
Comparing these options, we can see that Option 3: 3:1 is equivalent to the original ratio left-parenthesis 2 x minus 6 right-parenthesis colon left-parenthesis 6 x minus 4 right-parenthesis.