Simplify 5(7x−2)−14x+4 .
Using the distributive property, we have 5(7x-2) = 35x - 10. Thus, the expression becomes 35x - 10 - 14x + 4 = (35x - 14x) + (-10 + 4) = 21x - 6. Answer: \boxed{21x-6}.
Simplify 17d−33+9(2d+6)−11
Using the distributive property, we have:
17d - 33 + 9(2d + 6) - 11 = 17d - 33 + 18d + 54 - 11
Combining like terms, we get:
17d - 33 + 18d + 54 - 11 = (17d + 18d) + (-33 + 54 - 11) = 35d + 10
So, the simplified expression is \boxed{35d+10}.
Simplify 6(3q−4)+18−12q−7(4q+5) .
Using the distributive property, we have:
6(3q - 4) + 18 - 12q - 7(4q + 5) = 18q - 24 + 18 - 12q - 28q - 35
Combining like terms, we get:
18q - 24 + 18 - 12q - 28q - 35 = (18q - 12q - 28q) + (-24 + 18 - 35) = -22q - 41
So, the simplified expression is \boxed{-22q - 41}.
Simplify −5+3/4(8h+12)−10h .
Using the distributive property, we have:
-5 + \frac{3}{4}(8h + 12) - 10h = -5 + \frac{3}{4} \cdot 8h + \frac{3}{4} \cdot 12 - 10h
Simplifying the terms, we get:
-5 + \frac{3}{4} \cdot 8h + \frac{3}{4} \cdot 12 - 10h = -5 + 6h + 9 - 10h = (6h - 10h) + (-5 + 9)
Combining like terms, we have:
6h - 10h - 5 + 9 = -4h + 4
So, the simplified expression is \boxed{-4h + 4}.
Factor 24n−32 using the GCF
To factor out the greatest common factor (GCF) of 24n and -32, we need to determine the largest number that can divide both terms evenly.
First, let's find the prime factorization of each term:
24n: 2 * 2 * 2 * 3 * n
-32: -1 * 2 * 2 * 2 * 2 * 2
The GCF is 2 * 2 * 2, which is 8.
Factoring out the GCF, we have:
24n - 32 = 8 * (3n - 4)
Thus, the expression 24n - 32 can be factored as \boxed{8(3n - 4)}.