Question

1. \\(\frac{1}{4}k + \frac{1}{4}m - \frac{2}{3}k + \frac{5}{9}m\\)
2. \\(-4b + 2w + (-4b) + 8w\\)
3. \\(6 - 5z + 8 - 4z + 1\\)
4. inequalities

write an inequality that represents the situation: a large box of golf balls has more than 12 balls. describe how your inequality represents the situation.

Explanation:

Problem 8: Combine like terms in \(\frac{1}{4}k + \frac{1}{4}m - \frac{2}{3}k + \frac{5}{9}m\)

Step 1: Combine \(k\)-terms

Identify the terms with \(k\): \(\frac{1}{4}k\) and \(-\frac{2}{3}k\). Find a common denominator (12) to add them:
\(\frac{1}{4}k - \frac{2}{3}k = \frac{3}{12}k - \frac{8}{12}k = -\frac{5}{12}k\)

Step 2: Combine \(m\)-terms

Identify the terms with \(m\): \(\frac{1}{4}m\) and \(\frac{5}{9}m\). Find a common denominator (36) to add them:
\(\frac{1}{4}m + \frac{5}{9}m = \frac{9}{36}m + \frac{20}{36}m = \frac{29}{36}m\)

Step 3: Combine results

Combine the simplified \(k\)- and \(m\)-terms:
\(-\frac{5}{12}k + \frac{29}{36}m\)

Problem 9: Combine like terms in \(-4b + 2w + (-4b) + 8w\)

Step 1: Combine \(b\)-terms

Identify the terms with \(b\): \(-4b\) and \(-4b\). Add them:
\(-4b + (-4b) = -8b\)

Step 2: Combine \(w\)-terms

Identify the terms with \(w\): \(2w\) and \(8w\). Add them:
\(2w + 8w = 10w\)

Step 3: Combine results

Combine the simplified \(b\)- and \(w\)-terms:
\(-8b + 10w\)

Problem 10: Combine like terms in \(6 - 5z + 8 - 4z + 1\)

Step 1: Combine constant terms

Identify the constant terms: \(6\), \(8\), and \(1\). Add them:
\(6 + 8 + 1 = 15\)

Step 2: Combine \(z\)-terms

Identify the terms with \(z\): \(-5z\) and \(-4z\). Add them:
\(-5z - 4z = -9z\)

Step 3: Combine results

Combine the simplified constant and \(z\)-terms:
\(15 - 9z\)

Problem 11: Write an inequality for "A large box of golf balls has more than 12 balls"

Answer:

s:

1. \(\boldsymbol{-\frac{5}{12}k + \frac{29}{36}m}\)
2. \(\boldsymbol{-8b + 10w}\)
3. \(\boldsymbol{15 - 9z}\)
4. \(\boldsymbol{b > 12}\) (where \(b\) = number of golf balls)