Use the properties of operations to add 9(k+1/3)+10(1/2k−1) .(1 point)

To simplify the expression \( 9\left(k + \frac{1}{3}\right) + 10\left(\frac{1}{2}k - 1\right) \), we can use the distributive property to expand each term, and then combine like terms.

1. Distribute \(9\) and \(10\):

\[ 9\left(k + \frac{1}{3}\right) = 9k + 9 \cdot \frac{1}{3} = 9k + 3 \]

\[ 10\left(\frac{1}{2}k - 1\right) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10 \]

2. Now combine the results from both distributions:

\[ 9k + 3 + 5k - 10 \]

3. Combine the like terms (\(9k\) and \(5k\), as well as the constants \(3\) and \(-10\)):

\[ (9k + 5k) + (3 - 10) = 14k - 7 \]

Therefore, the simplified expression is:

\[ \boxed{14k - 7} \]

To simplify the expression \( 4(g - 2) + (g + 2) \), we will use the distributive property and then combine like terms.

1. Distribute the \(4\) in the first term:

\[ 4(g - 2) = 4g - 4 \cdot 2 = 4g - 8 \]

2. Now write the expression with the distributed term:

\[ 4g - 8 + (g + 2) \]

3. Distribute the parentheses in the second term:

\[ 4g - 8 + g + 2 \]

4. Combine like terms (\(4g\) and \(g\), as well as \(-8\) and \(2\)):

\[ (4g + g) + (-8 + 2) = 5g - 6 \]

Thus, the simplified expression is:

\[ \boxed{5g - 6} \]

To simplify the expression \((h + k) - (2k - h)\), follow these steps:

1. Distribute the negative sign across the second parentheses:

\[ (h + k) - (2k - h) = h + k - 2k + h \]

2. Combine like terms:

• For \(h\) terms: \(h + h = 2h\)
• For \(k\) terms: \(k - 2k = -k\)

Putting it all together:

\[ 2h - k \]

Thus, the simplified expression is:

\[ \boxed{2h - k} \]

To simplify the expression \((p - 3) - (2.4 + 2p)\), we'll follow these steps:

1. Distribute the negative sign across the second parentheses:

   \[ (p - 3) - (2.4 + 2p) = p - 3 - 2.4 - 2p \]

2. Combine like terms. Let's group \(p\) and \(-2p\), and \(-3\) and \(-2.4\):

   • For the \(p\) terms: \(p - 2p = -p\)
   • For the constant terms: \(-3 - 2.4 = -5.4\)

Now, putting it all together:

\[ -p - 5.4 \]

Thus, the simplified expression is:

\[ \boxed{-p - 5.4} \]

It looks like your expression contains some symbols that didn't translate well, possibly due to encoding issues. However, I’ll try to interpret it as best as I can.

Assuming you meant to subtract \(2(k - 4) - 3(2k - 1)\), let's work through the calculation step by step.

1. Distribute the coefficients:

   \[ 2(k - 4) = 2k - 8 \] \[ -3(2k - 1) = -3 \cdot 2k + 3 \cdot 1 = -6k + 3 \]

2. Combine the results of the distribution:

   \[ 2(k - 4) - 3(2k - 1) = (2k - 8) + (-6k + 3) \]

3. Combine like terms:

   • For \(k\) terms: \(2k - 6k = -4k\)
   • For constant terms: \(-8 + 3 = -5\)

Putting it all together, we get:

\[ -4k - 5 \]

Thus, the simplified expression is:

\[ \boxed{-4k - 5} \]

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