Simplify 5(7x−2)−14x+4
Simplify 17d−33+9(2d+6)−11
Simplify 6(3q−4)+18−12q−7(4q+5)
Simplify −5+3/4(8h+12)−10h .
Factor 24n−32 using the GCF.
Simplify −5 + 3/4(8h+12) − 10h
Simplify −5 + 3/4(8h + 12) − 10h
To simplify −5 + 3/4(8h + 12) − 10h:
First, distribute 3/4 to both terms inside the parentheses:
−5 + 3/4(8h) + 3/4(12) − 10h
Simplifying the terms inside the parentheses:
−5 + 6h + 9 - 10h
Next, combine like terms:
(6h - 10h) + (−5 + 9)
Simplifying further:
-4h + 4
The simplified expression is -4h + 4.
To simplify 5(7x-2)-14x+4, we can distribute the 5 to both terms inside the parentheses:
= 35x - 10 - 14x + 4
Next, we can combine like terms:
= (35x - 14x) + (-10 + 4)
= 21x - 6
To simplify 17d - 33 + 9(2d+6) - 11, we can distribute the 9 to the terms inside the parentheses:
= 17d - 33 + 9(2d) + 9(6) - 11
= 17d - 33 + 18d + 54 - 11
Next, we can combine like terms:
= (17d + 18d) + (-33 + 54 - 11)
= 35d + 10
To simplify 6(3q-4) + 18 - 12q - 7(4q+5), we can distribute the 6 and -7 to the terms inside the parentheses:
= 18q - 24 + 18 - 12q - 28q - 35
Next, we can combine like terms:
= (18q - 12q - 28q) + (-24 + 18 - 35)
= -22q - 41
To simplify -5 + 3/4(8h+12) - 10h, we can distribute the 3/4 to the terms inside the parentheses:
= -5 + 3/4(8h) + 3/4(12) - 10h
= -5 + 6h + 9/4 - 10h
Next, we can combine like terms:
= (6h - 10h) + (-5 + 9/4)
= -4h - 5/4
To factor 24n - 32 using the GCF (greatest common factor), we can determine that the GCF of 24 and 32 is 8. So we can factor out 8 from both terms:
= 8(3n - 4)
To simplify −5 + 3/4(8h+12) − 10h:
First, distribute 3/4 to both terms inside the parentheses:
−5 + 3/4(8h) + 3/4(12) − 10h
Simplifying the terms inside the parentheses:
−5 + 6h + 9 - 10h
Next, combine like terms:
(6h - 10h) + (−5 + 9)
Simplifying further:
-4h + 4
The simplified expression is -4h + 4.
To simplify the given expressions, we will apply the distributive property and combine like terms.
1. Simplify 5(7x−2)−14x+4:
Start by applying the distributive property: 5 * 7x = 35x and 5 * -2 = -10.
Now, rewrite the expression: 35x - 10 - 14x + 4.
Combine like terms by adding/subtracting the coefficients of similar terms: (35x - 14x) + (-10 + 4).
Simplify further: 21x - 6.
2. Simplify 17d−33+9(2d+6)−11:
First, apply the distributive property: 9 * 2d = 18d and 9 * 6 = 54.
Now, rewrite the expression: 17d - 33 + 18d + 54 - 11.
Combine like terms: (17d + 18d) + (-33 + 54 - 11).
Simplify further: 35d + 10.
3. Simplify 6(3q−4)+18−12q−7(4q+5):
Apply the distributive property: 6 * 3q = 18q and 6 * -4 = -24, as well as 7 * 4q = 28q and 7 * 5 = 35.
Now, rewrite the expression: 18q - 24 + 18 - 12q - 28q - 35.
Combine like terms: (18q - 12q - 28q) + (-24 + 18 - 35).
Simplify further: -22q - 41.
4. Simplify −5 + (3/4)(8h + 12) − 10h:
Start by applying the distributive property: (3/4) * 8h = (3/4) * 8h, and (3/4) * 12 = (3/4) * 12.
Now, rewrite the expression: -5 + (3/4) * 8h + (3/4) * 12 - 10h.
There are no like terms to combine, so we leave the expression as it is.
To factor 24n − 32 using the greatest common factor (GCF), we first identify the common factor. In this case, it is 8. Then, divide each term by 8.
Factor 24n − 32:
Divide 24n by 8: 24n/8 = 3n
Divide -32 by 8: -32/8 = -4
Rewrite the expression using the GCF: 8 * (3n - 4)
Therefore, the factored form of 24n − 32 is 8(3n - 4).