Question

Which expression is equivalent to 14y-12?

1) -14(y-1/2)
2) -14(y-12)
3) 1/4
4) 1/4(y - 1/2)
5) 1/4(y-2)

Answer 1

The expression
`\(14y - 12\)` is equivalent to itself (since it's already simplified), and it can also be rewritten in factored form as
`\(2(7y - 6)\)` .

None of the given options is correct

Step-by-step explanation:

To find an expression equivalent to
`\(14y - 12\)` , let's analyze each given option and simplify them when necessary:

1)
`\(-14(y - (1)/(2))\)`

Distributing the
`\(-14\)` into the parentheses, we get:

`\(-14 \cdot y + 14 \cdot (1)/(2) = -14y + 7\)`

This is not equivalent to
`\(14y - 12\)` , so option 1 is incorrect.

2)
`\(-14(y - 12)\)`

Again, distributing the
`\(-14\)` into the parentheses, we get:

`\(-14 \cdot y + 14 \cdot 12 = -14y + 168\)`

This is also not equivalent to
`\(14y - 12\)` , so option 2 is incorrect.

3)
`\((1)/(4)\)`

This option is just a constant and does not even contain the variable
`\(y\)`. Therefore, it cannot be equivalent to
`\(14y - 12\)` , which is a linear expression in
`\(y\)` . Option 3 is incorrect.

4)
`\((1)/(4)(y - (1)/(2))\)`

Distributing the
`\((1)/(4)\)` into the parentheses, we get:

`\((1)/(4) \cdot y - (1)/(4) \cdot (1)/(2) = (1)/(4)y - (1)/(8)\)`

This is not equivalent to
`\(14y - 12\)` , so option 4 is incorrect.

5 )
`\((1)/(4)(y - 2)\)`

Once again, distributing the
`\((1)/(4)\)` into the parentheses, we get:

`\((1)/(4) \cdot y - (1)/(4) \cdot 2 = (1)/(4)y - (1)/(2)\)`

This is not equivalent to
`\(14y - 12\)` , so option 5 is incorrect.

None of the given options 1) through 5) are equivalent to the expression
`\(14y - 12\)`.