Combine like terms to create an equivalent expression.\[{-\dfrac{4}{7}p+(-\dfrac27p)+\dfrac17}\]
The like terms are $-\dfrac47p$ and $-\dfrac27p$. Combining the coefficients of the like terms, we have $-\dfrac47p+(-\dfrac27p)=\boxed{-\dfrac67p}$.
To combine like terms, we add or subtract the coefficients of terms with the same variable.
The terms in the given expression are:
\(-\dfrac{4}{7}p, -\dfrac{2}{7}p, \dfrac{1}{7}\)
Since both \(-\dfrac{4}{7}p\) and \(-\dfrac{2}{7}p\) have \(p\) as the variable, we can add their coefficients to combine them.
\(-\dfrac{4}{7}p + \left( -\dfrac{2}{7} \right)p = -\dfrac{4}{7}p - \dfrac{2}{7}p = -\dfrac{6}{7}p\)
Now we can rewrite the expression with the combined like terms:
\(-\dfrac{6}{7}p + \dfrac{1}{7}\)
To combine like terms in this expression, we need to add or subtract the coefficients of the same variable. In this case, the variable is 'p'.
Let's simplify each term step by step:
The first term is \(-\dfrac{4}{7}p\).
The second term is \(-\dfrac{2}{7}p\).
And the third term is \(\dfrac{1}{7}\).
To combine the first two terms, we add the coefficients of 'p'. Since both terms have a 'p' as a variable, we can write them as \(-\dfrac{4}{7}p + (-\dfrac{2}{7}p)\).
To add these fractions, we need a common denominator, which is 7.
So, the expression becomes: \(\(-\dfrac{4}{7} - \dfrac{2}{7}\) times \(p\), which simplifies to \(-\dfrac{6}{7}p\).
Now let's combine this simplified term with the third term which is just \(\dfrac{1}{7}\) without a variable.
We simply write this as \(\dfrac{1}{7}\) because there is no other term to combine it with.
So, by combining like terms, the given expression \( - \dfrac{4}{7}p + (-\dfrac{2}{7}p) + \dfrac{1}{7}\) is equal to \(-\dfrac{6}{7}p + \dfrac{1}{7}\).