bot Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.(1 point)
To add the given expressions, we need to combine like terms.
First, let's simplify each term separately.
For the first term, 1/2(x + 4), we can distribute the 1/2 to the terms inside the parentheses:
1/2(x + 4) = 1/2 * x + 1/2 * 4 = (1/2)x + 2
For the second term, 1/4(4x - 2), we can distribute the 1/4 to the terms inside the parentheses:
1/4(4x - 2) = 1/4 * 4x + 1/4 * (-2) = x - 1/2
Now we can add the simplified terms:
(1/2)x + 2 + x - 1/2
Combining like terms:
(1/2 + 1)x + 2 - 1/2
(3/2)x + 3/2
To express the answer in mixed number form, we can divide the coefficient (3/2) by the denominator (2).
(3/2) ÷ 2 = 3/4
Therefore, the simplified expression in mixed number form is:
3/4x + 3/2
Add: (4d−3)+(12d+4) . (1 point)
To add the given expressions, we need to combine like terms:
(4d - 3) + (12d + 4)
In the first set of parentheses, there is a negative sign in front of 3. We can rewrite it as -3.
Now we can add the like terms:
4d + 12d - 3 + 4
Combining 4d and 12d gives us 16d:
16d - 3 + 4
Simplifying further:
16d + 1
Therefore, the simplified expression is:
16d + 1
Add: (2m−3)+(3n−1)+(3m+1) .(1 point)
To add the given expressions, we need to combine like terms:
(2m - 3) + (3n - 1) + (3m + 1)
First, let's group the terms that have the same variables together:
(2m + 3m) + (-3 - 1 + 1) + (3n)
Combining like terms:
(5m) + (-3 - 1 + 1) + (3n)
Simplifying further:
(5m) + (-3 + 1) + (3n)
(-3 + 1) simplifies to -2:
(5m) - 2 + (3n)
Therefore, the simplified expression is:
5m - 2 + 3n
wrong
Apologies for the mistake. Let's go through the addition again:
To add the given expressions, we need to combine like terms:
(2m - 3) + (3n - 1) + (3m + 1)
First, let's group the terms that have the same variables together:
(2m + 3m) + (-3 + 1) + (3n + 1)
Combining like terms:
5m - 2 + 3n + 1
Now, let's simplify further:
5m + 3n - 1
Therefore, the simplified expression is:
5m + 3n - 1
wrong!
Apologies for the misunderstanding. Let's go through the addition again:
To add the given expressions, we need to combine like terms:
(2m - 3) + (3n - 1) + (3m + 1)
First, let's group the terms that have the same variables together:
(2m + 3m) + (-3 + 1) + (3n + 1)
Combining like terms:
5m - 2 + 3n + 1
Now, let's simplify further:
5m + 3n - 1
Therefore, the simplified expression is:
5m + 3n - 1
no just add them together
Apologies for the confusion. To add the given expressions directly, we can combine the like terms together.
(2m - 3) + (3n - 1) + (3m + 1)
Combine the like terms:
(2m + 3m) + (-3 + 1) + (3n + 1)
5m - 2 + 3n + 1
Combine the coefficients:
5m + 3n + (-2 + 1)
Simplify the constants:
5m + 3n - 1
Therefore, the simplified expression is:
5m + 3n - 1
NO!
Apologies for the repeated errors. Let's add the expressions correctly:
(2m - 3) + (3n - 1) + (3m + 1)
Add the like terms:
(2m + 3m + 3n) + (-3 - 1 + 1)
Combine the coefficients:
(5m + 3n) + (-3)
Simplify:
5m + 3n - 3
Therefore, the simplified expression is:
5m + 3n - 3
Subtract: 2(10b+4)−(b−2) .(1 point)
To subtract the given expression, we need to distribute and simplify:
2(10b + 4) - (b - 2)
First, let's distribute the 2 to each term inside the parentheses:
2 * 10b + 2 * 4 - (b - 2)
20b + 8 - (b - 2)
Next, let's distribute the negative sign to each term inside the second set of parentheses:
20b + 8 - b + 2
Combining like terms:
(20b - b) + (8 + 2)
19b + 10
Therefore, the simplified expression is:
19b + 10
Subtract: (3g−4)−2(3g+4) .(1 point)
To subtract the given expression, we need to distribute and simplify:
(3g - 4) - 2(3g + 4)
First, let's distribute the -2 to each term inside the second set of parentheses:
3g - 4 - 2 * 3g - 2 * 4
Next, let's simplify:
3g - 4 - 6g - 8
Combine like terms:
(3g - 6g) + (-4 - 8)
-3g - 12
Therefore, the simplified expression is:
-3g - 12
Use the properties of operations to add 9(k+1/3)+10(1/2k−1) .(1 point)
Responses
14k−23
14 k minus Start Fraction 2 over 3 End Fraction
14k−7
14 k minus 7
1912k−23
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction
14k+13
To add the given expression, 9(k + 1/3) + 10(1/2k - 1), we can simplify each term separately and then combine them.
For the first term, 9(k + 1/3), we can distribute the 9 to the terms inside the parentheses:
9 * k + 9 * 1/3 = 9k + 3
For the second term, 10(1/2k - 1), we can distribute the 10 to the terms inside the parentheses:
10 * 1/2k - 10 * 1 = 5k - 10
Now, let's add the simplified terms together:
(9k + 3) + (5k - 10)
Combining like terms:
9k + 5k + 3 - 10
14k - 7
Therefore, the simplified expression is:
14k - 7
Use the properties of operations to add 4(g−2)+(g+2) .(1 point)
Responses
5g+10
5 g plus 10
5g
5 g
5g−6
5 g minus 6
5g−10
To add the given expressions, 4(g - 2) + (g + 2), we need to distribute and combine like terms.
First, let's distribute the 4 to the terms inside the first set of parentheses:
4 * g - 4 * 2 = 4g - 8
Now, let's simplify the expression:
(4g - 8) + (g + 2)
Combine like terms:
4g + g - 8 + 2
Combine the coefficients:
(4g + g) - 6
Simplify the expression:
5g - 6
Therefore, the simplified expression is:
5g - 6.
Use the properties of operations to subtract (h+k)−(2k−h) .(1 point)
Responses
−k
negative k
2h+k
2 h plus k
−2h−k
negative 2 h minus k
2h−k
To subtract the given expressions, (h + k) - (2k - h), we need to distribute and combine like terms.
First, let's distribute the negative sign to each term inside the second set of parentheses:
(h + k) - (2k - h) = h + k - 2k + h
Now, let's combine like terms:
(h + h) + (k - 2k)
Simplify the expression:
2h + (-k)
Therefore, the simplified expression is:
2h - k.
Use the properties of operations to subtract (p−3)−(2.4+2p) .(1 point)
Responses
p−5.4
p minus 5.4
−p+5.4
negative p plus 5.4
3p−5.4
3 p minus 5.4
−p−5.4
To subtract the given expressions, (p - 3) - (2.4 + 2p), we need to distribute and combine like terms.
First, let's distribute the negative sign to each term inside the second set of parentheses:
(p - 3) - (2.4 + 2p) = p - 3 - 2.4 - 2p
Now, let's combine like terms:
(p - 2p) - (3 + 2.4)
Simplify the expression:
-p - 3 - 2.4
Combine the constants:
-p - 5.4
Therefore, the simplified expression is:
-p - 5.4.
Subtract: 2(k−4)−3(2k−1) .(1 point)
Responses
−4k−5
negative 4 k minus 5
−4k−11
negative 4 k minus 11
−6k−18
negative 6 k minus 18
8k−11
To subtract the given expressions, 2(k - 4) - 3(2k - 1), we need to distribute and combine like terms.
First, let's distribute the 2 and the 3 to the terms inside the first and second set of parentheses respectively:
2 * k - 2 * 4 - 3 * 2k + 3 * 1
Simplify the expression:
2k - 8 - 6k + 3
Now, let's combine like terms:
(2k - 6k) + (-8 + 3)
Combine the coefficients:
-4k - 5
Therefore, the simplified expression is:
-4k - 5.