Simplify 5(7x−2)−14x+4
Simplify 17d−33+9(2d+6)−11
Simplify 6(3q−4)+18−12q−7(4q+5)
Simplify −5+34(8h+12)−10h .
Factor 24n−32 using the GCF.
To simplify 5(7x−2)−14x+4, we first distribute the 5 to each term inside the parentheses:
5 * 7x = 35x
5 * (-2) = -10
So the expression becomes: 35x - 10 - 14x + 4.
Next, we combine the like terms:
35x - 14x = 21x
-10 + 4 = -6
So the simplified expression is 21x - 6.
To simplify 17d−33+9(2d+6)−11, we first distribute the 9 to each term inside the parentheses:
9 * 2d = 18d
9 * 6 = 54
So the expression becomes: 17d - 33 + 18d + 54 - 11.
Next, we combine the like terms:
17d + 18d = 35d
-33 + 54 - 11 = 10
So the simplified expression is 35d + 10.
To simplify 6(3q−4)+18−12q−7(4q+5), we first distribute the 6 to each term inside the first parentheses:
6 * 3q = 18q
6 * (-4) = -24
So the expression becomes: 18q - 24 + 18 - 12q - 7(4q + 5).
Next, we distribute the -7 to each term inside the second parentheses:
-7 * 4q = -28q
-7 * 5 = -35
So the expression becomes: 18q - 24 + 18 - 12q - 28q - 35.
Next, we combine the like terms:
18q - 12q - 28q = -22q
-24 + 18 - 35 = -41
So the simplified expression is -22q - 41.
To simplify −5+34(8h+12)−10h, we first distribute the 34 to each term inside the parentheses:
34 * 8h = 272h
34 * 12 = 408
So the expression becomes: -5 + 272h + 408 - 10h.
Next, we combine the like terms:
272h - 10h = 262h
-5 + 408 = 403
So the simplified expression is 262h + 403.
To factor 24n−32 using the GCF, we first find the greatest common factor (GCF) of the terms 24n and 32, which is 8.
Next, we divide each term by the GCF, 8.
24n ÷ 8 = 3n
32 ÷ 8 = 4
So the expression becomes: 8(3n - 4).
Therefore, we can factor 24n−32 as 8(3n - 4).
1/4+2/3
1/5x1/3
1/2-5/10
1/4 divvided by 7/10
To simplify 1/4 + 2/3, we need to find a common denominator. The least common multiple of 4 and 3 is 12. We can then rewrite the fractions with the common denominator:
1/4 becomes 3/12 (multiply numerator and denominator by 3)
2/3 becomes 8/12 (multiply numerator and denominator by 4)
Now we can add the fractions:
3/12 + 8/12 = 11/12
So, 1/4 + 2/3 simplifies to 11/12.
To simplify 1/5 * 1/3, we simply multiply the numerators together and the denominators together:
(1 * 1) / (5 * 3) = 1/15
So, 1/5 times 1/3 simplifies to 1/15.
To simplify 1/2 - 5/10, we need to find a common denominator. The least common multiple of 2 and 10 is 10. We can then rewrite the fractions with the common denominator:
1/2 becomes 5/10 (multiply numerator and denominator by 5)
Now we can subtract the fractions:
5/10 - 5/10 = 0/10 = 0
So, 1/2 - 5/10 simplifies to 0.
To simplify 1/4 divided by 7/10, we can multiply by the reciprocal of the second fraction:
(1/4) / (7/10) = (1/4) * (10/7) = 10/28
We can simplify 10/28 by dividing both the numerator and denominator by their greatest common factor, which is 2:
(10/2) / (28/2) = 5/14
So, 1/4 divided by 7/10 simplifies to 5/14.
Simplify −5+34(8h+12)−10h
To simplify −5+34(8h+12)−10h, we first distribute the 34 to each term inside the parentheses:
34 * 8h = 272h
34 * 12 = 408
So the expression becomes: -5 + 272h + 408 - 10h.
Next, we combine like terms:
272h - 10h = 262h
So the simplified expression is 262h + 403.
Therefore, −5+34(8h+12)−10h simplifies to 262h + 403.
−5+3/4(8h+12)−10h
To simplify −5+3/4(8h+12)−10h, we first distribute the 3/4 to each term inside the parentheses:
(3/4) * 8h = 6h
(3/4) * 12 = 9
So the expression becomes: -5 + 6h + 9 - 10h.
Next, we combine like terms:
6h - 10h = -4h
So the simplified expression is -4h + 4.
Therefore, −5+3/4(8h+12)−10h simplifies to -4h + 4.
−5+3/4(8h+12)−10h,
Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23 - 9(2x + 5) + 11 * x' (1 point)
1. 23 - 18x - 45 + 11x
2. 14(2x + 5) + 11x
3. 23 - 7x - 4 + 11x
4. 14(2x + 5 + 11x)
To simplify the given expressions, we will use the basic rules of simplifying algebraic expressions.
1. Simplify 5(7x−2)−14x+4:
Start by distributing the 5 to the terms inside the parentheses:
5(7x) - 5(2) - 14x + 4
This becomes:
35x - 10 - 14x + 4
Now, combine like terms:
(35x - 14x) + (-10 + 4)
This simplifies to:
21x - 6
2. Simplify 17d−33+9(2d+6)−11:
Start by distributing the 9 to the terms inside the parentheses:
17d - 33 + 9(2d) + 9(6) - 11
This becomes:
17d - 33 + 18d + 54 - 11
Now, combine like terms:
(17d + 18d) + (-33 + 54 - 11)
This simplifies to:
35d + 10
3. Simplify 6(3q−4)+18−12q−7(4q+5):
Start by distributing the 6 to the terms inside the first set of parentheses, and distributing the -7 to the terms inside the second set of parentheses:
6(3q) - 6(4) + 18 - 12q - 7(4q) - 7(5)
This becomes:
18q - 24 + 18 - 12q - 28q - 35
Now, combine like terms:
(18q - 12q - 28q) + (-24 + 18 - 35)
This simplifies to:
-22q - 41
4. Simplify −5+34(8h+12)−10h:
Start by distributing the 34 to the terms inside the parentheses:
-5 + 34(8h) + 34(12) - 10h
This becomes:
-5 + 272h + 408 - 10h
Now, combine like terms:
(-5 - 10h) + (272h + 408)
This simplifies to:
262h + 403
For factoring 24n - 32 using the GCF (Greatest Common Factor):
First, find the GCF of 24 and 32, which is 8.
Then, divide each term by the GCF (8):
(24n ÷ 8) - (32 ÷ 8)
This becomes:
3n - 4
Therefore, the factored form of 24n - 32 is 3n - 4.