Simplify 5(7x−2)−14x+4

Question

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.

Answer 1

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).

Answer 2

1/4+2/3
1/5x1/3
1/2-5/10
1/4 divvided by 7/10

Answer 3

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.

Answer 4

Simplify −5+34(8h+12)−10h

Answer 5

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.

Answer 6

−5+3/4(8h+12)−10h

Answer 7

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.

Answer 8

−5+3/4(8h+12)−10h,

Answer 9

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)