Question

which pair of expressions below are equivalent? answer attempt 1 out of 3 \\( 9x + 7x \\) and \\( 16x \\) \\( 9(7x - 5) \\) and \\( 63x - 5 \\) \\( 9x + 7x \\) and \\( 16x^2 \\) \\( 9x - 7y \\) and \\( 7y - 9x \\)

Explanation:

Step1: Analyze first option

For \(9x + 7x\), we combine like terms. The coefficient of \(x\) in \(9x\) is 9 and in \(7x\) is 7. So \(9x+7x=(9 + 7)x=16x\). So \(9x + 7x\) and \(16x\) are equivalent.

Step2: Analyze second option

Using the distributive property \(a(b - c)=ab - ac\), for \(9(7x-5)\), we have \(9\times7x-9\times5 = 63x-45\), which is not equal to \(63x - 5\).

Step3: Analyze third option

\(9x+7x=(9 + 7)x = 16x\), and \(16x^{2}\) is \(16\times x\times x\), which is not equal to \(16x\) (unless \(x = 0\) or \(x = 1\), but generally they are not equivalent).

Step4: Analyze fourth option

\(9x-7y=-(7y - 9x)\), which is the negative of \(7y - 9x\), so they are not equivalent.

Answer:

A. \(9x + 7x\) and \(16x\)