Use the properties of operations to add 9(k+1/3)+10(1/2k−1) .(1 point)
To add these expressions, we can use the distributive property to multiply the coefficients with the terms inside the parentheses and then combine like terms.
First, let's distribute 9 to (k + 1/3):
9(k + 1/3) = 9k + 9/3 = 9k + 3
Next, let's distribute 10 to (1/2k - 1):
10(1/2k - 1) = 10/2k - 10 = 5k - 10
Now we can combine like terms by adding 9k + 3 and 5k - 10:
(9k + 3) + (5k - 10) = 9k + 5k + 3 - 10 = 14k - 7
Therefore, 9(k+1/3) + 10(1/2k−1) simplifies to 14k - 7.
Use the properties of operations to add 4(g−2)+(g+2) .(1 point)
To add these expressions, we can use the distributive property to multiply the coefficients with the terms inside the parentheses and then combine like terms.
First, let's distribute 4 to (g - 2):
4(g - 2) = 4g - 8
Next, let's distribute 1 to (g + 2):
1(g + 2) = g + 2
Now we can combine like terms by adding 4g - 8 and g + 2:
(4g - 8) + (g + 2) = 4g + g - 8 + 2 = 5g - 6
Therefore, 4(g-2) + (g+2) simplifies to 5g - 6.
Use the properties of operations to subtract (h+k)−(2k−h) .(1 point)
To subtract these expressions, we can use the distributive property to distribute the negative sign to every term inside the parentheses and then combine like terms.
First, let's distribute the negative sign to (2k - h):
-(2k - h) = -2k + h
Now we can rewrite the expression as:
(h + k) - (2k - h)
Let's distribute the negative sign to every term inside the second set of parentheses:
(h + k) + (-2k + h)
Now we can combine like terms by adding h + h, and k + (-2k):
(h + k) + (-2k + h) = 2h + (-k)
Finally, we can write the expression as:
2h - k
Therefore, (h+k)−(2k−h) simplifies to 2h - k.
Use the properties of operations to subtract (p−3)−(2.4+2p) .(1 point)
To subtract these expressions, we can use the distributive property to distribute the negative sign to every term inside the second set of parentheses and then combine like terms.
First, let's distribute the negative sign to (2.4 + 2p):
-(2.4 + 2p) = -2.4 - 2p
Now we can rewrite the expression as:
(p - 3) - (2.4 + 2p)
Let's distribute the negative sign to every term inside the second set of parentheses:
(p - 3) + (-2.4 - 2p)
Now we can combine like terms by adding p + (-2p), and -3 + (-2.4):
(p - 3) + (-2.4 - 2p) = -p - 5.4
Finally, we can simplify the expression to:
-p - 5.4
Therefore, (p-3)-(2.4+2p) simplifies to -p - 5.4.
Subtract: 2(k−4)−3(2k−1) .(1 point)
To subtract these expressions, we can use the distributive property to distribute the coefficients to the terms inside the parentheses and then combine like terms.
First, let's distribute 2 to (k - 4):
2(k - 4) = 2k - 8
Next, let's distribute -3 to (2k - 1):
-3(2k - 1) = -6k + 3
Now we can rewrite the expression as:
2k - 8 - (6k - 3)
To subtract the expressions, we should distribute the negative sign to every term inside the second set of parentheses:
2k - 8 - 6k + 3
Finally, we can combine like terms by adding 2k - 6k, and -8 + 3:
2k - 8 - 6k + 3 = -4k - 5
Therefore, 2(k-4) - 3(2k-1) simplifies to -4k - 5.
To add the given expression, 9(k+1/3) + 10(1/2k-1), we need to distribute the coefficients (9 and 10) to the terms inside the parentheses and then combine like terms.
Let's start by distributing the coefficients:
9(k+1/3) = 9k + 9(1/3) = 9k + 3
10(1/2k-1) = 10(1/2k) - 10(1) = 10/2k - 10 = 5k - 10
Now, we can combine the like terms:
9k + 3 + 5k - 10
Combine the k terms: 9k + 5k = 14k
Combine the constant terms: 3 - 10 = -7
So the final expression becomes:
14k - 7