Question

1. simplify $-5(7 + x) + 2\frac{5}{6}x$.

Explanation:

Step1: Distribute -5

First, we use the distributive property \(a(b + c)=ab+ac\) to expand \(-5(7 + x)\). So we get \(-5\times7+(-5)\times x=-35 - 5x\).

Step2: Convert mixed number to improper fraction

Next, we convert the mixed number \(2\frac{5}{6}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{ac + b}{c}\), so \(2\frac{5}{6}=\frac{2\times6 + 5}{6}=\frac{17}{6}\). So the term \(2\frac{5}{6}x\) becomes \(\frac{17}{6}x\).

Step3: Combine like terms

Now we combine the \(x\) terms. We have \(-5x+\frac{17}{6}x\). First, we write \(-5\) as \(-\frac{30}{6}\) (since \(-5 =-\frac{30}{6}\)) to have a common denominator. Then \(-\frac{30}{6}x+\frac{17}{6}x=\frac{-30 + 17}{6}x=\frac{-13}{6}x=-2\frac{1}{6}x\). And we still have the constant term \(-35\). So the simplified expression is \(-35-2\frac{1}{6}x\) (or \(-35-\frac{13}{6}x\)).

Answer:

\(-35 - \frac{13}{6}x\) (or \(-35-2\frac{1}{6}x\))