Add the linear expressions: 7(n−2)+5(n+4)+3(n+1) .(1 point)

Question

Responses

15n+9
15 n plus 9

3n+3
3 n plus 3

15n
15 n

15n+3

Answer 1

To add the linear expressions \( 7(n-2) + 5(n+4) + 3(n+1) \), we will first distribute the constants across the parentheses:

1. Distributing \( 7 \) in the first term: \[ 7(n - 2) = 7n - 14 \]

2. Distributing \( 5 \) in the second term: \[ 5(n + 4) = 5n + 20 \]

3. Distributing \( 3 \) in the third term: \[ 3(n + 1) = 3n + 3 \]

Now we will combine all of these results: \[ 7n - 14 + 5n + 20 + 3n + 3 \]

Next, we will combine the like terms (the \( n \) terms and the constant terms):

• For the \( n \) terms: \[ 7n + 5n + 3n = 15n \]

• For the constant terms: \[ -14 + 20 + 3 = 9 \]

Putting it all together, we get: \[ 15n + 9 \]

So the final answer is: \[ \boxed{15n + 9} \]

Answer 2

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Answer 3

To subtract the expression \( (j + 2) - 2(3 - 9j) \), we first start by distributing the \(-2\) across the second term:

1. Distributing \(-2\) in the second term: \[ -2(3 - 9j) = -2 \cdot 3 + (-2) \cdot (-9j) = -6 + 18j \]

Now we rewrite the original expression incorporating this distribution: \[ (j + 2) - (6 - 18j) \]

Now, we can rewrite it without the parentheses: \[ j + 2 - 6 + 18j \]

Next, we combine the like terms:

• For the \(j\) terms: \[ j + 18j = 19j \]

• For the constant terms: \[ 2 - 6 = -4 \]

Putting these together, we get: \[ 19j - 4 \]

Thus, the final answer is: \[ \boxed{19j - 4} \]

Answer 4

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Answer 5

To subtract the expression \( (2u - 7y) - (7u + 2y) \), we will first distribute the negative sign across the second term:

1. Rewrite the expression: \[ (2u - 7y) - (7u + 2y) = 2u - 7y - 7u - 2y \]

Now we combine like terms:

• Combine the \(u\) terms: \[ 2u - 7u = -5u \]

• Combine the \(y\) terms: \[ -7y - 2y = -9y \]

Putting it all together, we have: \[ -5u - 9y \]

Thus, the final answer is: \[ \boxed{-5u - 9y} \]

Answer 6

Simplify 9+3(4a−7)−5a+6 (1 point)
Responses

43a+78
43 a plus 78

43a−78
43 a minus 78

7a−6
7 a minus 6

7a+6

Answer 7

To simplify the expression \( 9 + 3(4a - 7) - 5a + 6 \), we will follow these steps:

1. Distribute the 3 in the term \( 3(4a - 7) \): \[ 3(4a - 7) = 12a - 21 \]

2. Substitute this back into the expression: \[ 9 + (12a - 21) - 5a + 6 \]

3. Combine like terms:

   • Combine the \(a\) terms: \[ 12a - 5a = 7a \]
   • Combine the constant terms: \[ 9 - 21 + 6 = -12 + 6 = -6 \]

4. Put everything together: \[ 7a - 6 \]

So the final simplified expression is: \[ \boxed{7a - 6} \]