To determine whether the pair of expressions is equivalent, let's look at each one carefully:
1. \(\frac{9x + 5}{5}\)
2. \(9x\)
Let's analyze these two expressions:
1. \(\frac{9x + 5}{5}\): This expression means that the entire quantity \(9x + 5\) is divided by 5.
2. \(9x\): This expression is simply nine times \(x\), without any division.
For these two expressions to be equivalent, they must yield the same value for any value of \(x\).
Let's see if they do:
If you plug \(x = 1\):
1. \(\frac{9(1) + 5}{5} = \frac{9 + 5}{5} = \frac{14}{5} = 2.8\)
2. \(9(1) = 9\)
Clearly, \(\frac{14}{5} \neq 9\).
For any value of \(x\), the expressions will not yield the same value because the first expression involves both \(x\) and an additional constant term (5), which is being divided by 5 along with \(9x\).
Therefore, \(\frac{9x + 5}{5}\) and \(9x\) are not equivalent expressions.
tell whether this pair of expressions is equivalent.
the quantity nine x plus five divided by five and nine x
1 answer