6(3q - 4) + 18 - 12q - 7(4q + 5)
Let's simplify the expression step by step:
6(3q - 4) + 18 - 12q - 7(4q + 5)
First, we distribute the 6 to the terms inside the first parentheses:
18q - 24 + 18 - 12q - 7(4q + 5)
Next, we distribute the -7 to the terms inside the second parentheses:
18q - 24 + 18 - 12q - 28q - 35
Now, we combine like terms:
(18q - 12q - 28q) + (-24 + 18 - 35)
This simplifies to:
-22q - 41
-5 + 3/4(8h + 12) - 10h
Let's simplify the expression step by step:
-5 + 3/4(8h + 12) - 10h
First, we simplify the parentheses:
-5 + 3/4 * 8h + 3/4 * 12 - 10h
Next, we distribute the 3/4 to the terms inside the parentheses:
-5 + (3/4)(8h) + (3/4)(12) - 10h
This simplifies to:
-5 + (6h) + (9) - 10h
Now, we combine like terms:
(6h - 10h) + (-5 + 9)
Simplifying further:
-4h + 4
Therefore, the simplified expression is -4h + 4.
24n - 32 GCF
To determine the greatest common factor (GCF) of 24n and 32, we need to factorize both numbers.
The prime factorization of 24 is 2^3 * 3 * 1.
The prime factorization of 32 is 2^5 * 1.
To find the greatest common factor, we need to find the highest power of each prime factor that appears in both numbers.
The GCF of 24n and 32 is 2^3 = 8.
Therefore, the greatest common factor of 24n and 32 is 8.
Factor 24n - 32 using the GCF
To factor 24n - 32 using the greatest common factor (GCF), we first need to determine the GCF of the terms.
The GCF of 24n and 32 is 8.
Now, we can factor out the GCF from each term:
24n - 32 = 8(3n - 4)
Therefore, the factored form of 24n - 32 using the GCF is 8(3n - 4).
23 - 9(2x + 5) + 11x
Let's simplify the expression step by step:
23 - 9(2x + 5) + 11x
First, we distribute the -9 to the terms inside the parentheses:
23 - 9 * 2x - 9 * 5 + 11x
This simplifies to:
23 - 18x - 45 + 11x
Next, we combine like terms:
(-18x + 11x) + (23 - 45)
Simplifying further:
-7x - 22
Therefore, the simplified expression is -7x - 22.