Question

Simplfy 17d-33+9(2d+6)-11
GPT-4o mini
To simplify the expression \( 17d - 33 + 9(2d + 6) - 11 \), follow these steps:

1. Distribute the \( 9 \) into the parentheses:
\[
9(2d + 6) = 9 \cdot 2d + 9 \cdot 6 = 18d + 54
\]

2. Substitute this back into the expression:
\[
17d - 33 + 18d + 54 - 11
\]

3. Now combine like terms:
- Combine the \( d \) terms:
\[
17d + 18d = 35d
\]
- Combine the constant terms:
\[
-33 + 54 - 11 = -33 + 43 = 10
\]

4. Now, put it all together:
\[
35d + 10
\]

So, the simplified expression is:
\[
\boxed{35d + 10}
\]
simplify 6(3q-4)+18-12q-7(4q+5)
GPT-4o mini
To simplify the expression \( 6(3q - 4) + 18 - 12q - 7(4q + 5) \), follow these steps:

1. Distribute the terms inside the parentheses:
- For \( 6(3q - 4) \):
\[
6 \cdot 3q - 6 \cdot 4 = 18q - 24
\]
- For \( -7(4q + 5) \):
\[
-7 \cdot 4q - 7 \cdot 5 = -28q - 35
\]

2. Substitute these back into the expression:
\[
(18q - 24) + 18 - 12q + (-28q - 35)
\]

3. Combine like terms:
- Combine the \( q \) terms:
\[
18q - 12q - 28q = (18 - 12 - 28)q = -22q
\]
- Combine the constant terms:
\[
-24 + 18 - 35 = -24 + 18 - 35 = -6 - 35 = -41
\]

4. Putting it all together, the expression becomes:
\[
-22q - 41
\]

So, the simplified expression is:
\[
\boxed{-22q - 41}
\]
Simplify -5+3/4(8h+12)-10h
GPT-4o mini
To simplify the expression \(-5 + \frac{3}{4}(8h + 12) - 10h\), follow these steps:

1. Distribute \(\frac{3}{4}\) into the parentheses:
\[
\frac{3}{4}(8h + 12) = \frac{3}{4} \cdot 8h + \frac{3}{4} \cdot 12
\]
Calculating each term:
\[
\frac{3}{4} \cdot 8h = 6h
\]
\[
\frac{3}{4} \cdot 12 = 9
\]

So, \(\frac{3}{4}(8h + 12) = 6h + 9\).

2. Substitute this back into the expression:
\[
-5 + (6h + 9) - 10h
\]

3. Now combine like terms:
- Combine the \(h\) terms:
\[
6h - 10h = -4h
\]
- Combine the constant terms:
\[
-5 + 9 = 4
\]

4. Putting it all together, the expression becomes:
\[
-4h + 4
\]

Thus, the simplified expression is:
\[
\boxed{-4h + 4}
\]
Factor 24n-32 using only GCF.
GPT-4o mini
To factor the expression \( 24n - 32 \) using the greatest common factor (GCF), follow these steps:

1. **Find the GCF of the coefficients**: The coefficients are \( 24 \) and \( 32 \).
- The prime factorization of \( 24 \) is \( 2^3 \times 3 \).
- The prime factorization of \( 32 \) is \( 2^5 \).
- The GCF is the product of the lowest powers of the common prime factors. Here, the common factor is \( 2 \), and the lowest power is \( 2^3 = 8 \).

2. **Factor out the GCF**:
\[
24n - 32 = 8(3n) - 8(4) = 8(3n - 4)
\]

Thus, the factored form of \( 24n - 32 \) is:
\[
\boxed{8(3n - 4)}
\]
simplify 23-9(2x+5)+11x
GPT-4o mini
To simplify the expression \( 23 - 9(2x + 5) + 11x \), follow these steps:

1. **Distribute** \(-9\) into the parentheses:
\[
-9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45
\]

2. **Substitute this back into the expression**:
\[
23 - 18x - 45 + 11x
\]

3. **Combine like terms**:
- Combine the \(x\) terms:
\[
-18x + 11x = -7x
\]
- Combine the constant terms:
\[
23 - 45 = -22
\]

4. **Putting it all together**:
\[
-7x - 22
\]

Therefore, the simplified expression is:
\[
\boxed{-7x - 22}
\]
do it using distriputive property
GPT-4o mini
Certainly! Let's simplify \( 23 - 9(2x + 5) + 11x \) using the distributive property step-by-step.

1. **Apply the distributive property** to distribute \(-9\) into the parentheses:
\[
-9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45
\]

2. **Rewrite the expression** with this substitution:
\[
23 - 18x - 45 + 11x
\]

3. **Now, combine like terms**:
- Combine the \(x\) terms:
\[
-18x + 11x = -7x
\]
- Combine the constant terms:
\[
23 - 45 = -22
\]

4. **Putting it all together**, we have:
\[
-7x - 22
\]

So, using the distributive property, the simplified expression is:
\[
\boxed{-7x - 22}
\]