Remember that to simplify an expression with multiple operations, we need to deal with the parenthesis first. To do it, we are going to apply the distributive property: \(a(b+c)=ab+ac\); in other words, we first distribute (multiply) \(a\) to \(b\), and then we distribute (multiply) \(a\) to \(c\).
Let's apply the property to our expression with \(a=\frac{2}{3}\), \(b=12c\), and \(c=-9\):
\(\frac{2}{3} (12c-9)+14c\)
\(\frac{2}{3} *12c-\frac{2}{3} *9+14c\)
\(8c-6 +14c\)
Now, we are going to group like terms; like terms are terms whose variables and exponents are the same, in our case, the terms with the variable \(c\)
\(8c-6 +14c\)
\(8c+14c-6\)
Now we just need to simplify our like terms:
\(22c-6\)
We can conclude that the simplified form of the expression \(\frac{2}{3} (12c-9)+14c\) is \(22c-6\).
