Add and Subtract Algebraic Expressions Quick Check

Question

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Question
Use the properties of operations to add 9(k+1/3)+10(1/2k−1) .(1 point)
Responses

19 1/2k−2/3
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction

1/4k−2/3
14 k minus Start Fraction 2 over 3 End Fraction

1/4k−7
14 k minus 7

1/4k+13
14 k plus 13
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page 16 of 16

Answer 1

To add the expression \( 9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1) \), we'll first distribute the constants (9 and 10) across the terms in the parentheses.

1. Distributing: \[ 9(k) + 9\left(\frac{1}{3}\right) + 10\left(\frac{1}{2}k\right) - 10(1) \] becomes: \[ 9k + 3 + 5k - 10 \]

2. Next, combine like terms:

   • Combine the \(k\) terms: \(9k + 5k = 14k\)
   • Combine the constant terms: \(3 - 10 = -7\)

So, the expression simplifies to: \[ 14k - 7 \]

Out of the provided options, the correct answer is: \(14k - 7\).

Answer 2

Use the properties of operations to add 4(g−2)+(g+2) .(1 point)
Responses

5g−6
5 g minus 6

5g+10
5 g plus 10

5g
5 g

5g−10

Answer 3

To add the expression \( 4(g - 2) + (g + 2) \), we will first distribute the 4 across the terms in the first parentheses.

1. Distributing: \[ 4(g) - 4(2) + (g + 2) \] becomes: \[ 4g - 8 + g + 2 \]

2. Next, combine like terms:

   • Combine the \(g\) terms: \(4g + g = 5g\)
   • Combine the constant terms: \(-8 + 2 = -6\)

So, the expression simplifies to: \[ 5g - 6 \]

Out of the provided options, the correct answer is: \(5g - 6\).

Answer 4

Use the properties of operations to subtract (h+k)−(2k−h) .(1 point)
Responses

−k
negative k

−2h−k
negative 2 h minus k

2h−k
2 h minus k

2h+k

Answer 5

To simplify the expression \( (h + k) - (2k - h) \), we first distribute the negative sign across the second parentheses.

1. Rewrite the expression: \[ (h + k) - (2k - h) = (h + k) - 2k + h \]

2. Combine like terms:

   • Combine the \( h \) terms: \( h + h = 2h \)
   • Combine the \( k \) terms: \( k - 2k = -k \)

So, the expression simplifies to: \[ 2h - k \]

Out of the provided options, the correct answer is: \(2h - k\).

Answer 6

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

Answer 7

To simplify the expression \( (p - 3) - (2.4 + 2p) \), we start by distributing the negative sign to the terms inside the second parentheses.

1. Rewrite the expression: \[ (p - 3) - (2.4 + 2p) = p - 3 - 2.4 - 2p \]

2. Combine like terms:

   • Combine the \( p \) terms: \( p - 2p = -p \)
   • Combine the constant terms: \( -3 - 2.4 = -5.4 \)

So, the expression simplifies to: \[ -p - 5.4 \]

Out of the provided options, the correct answer is: \(-p - 5.4\).

Answer 8

Subtract: 2(k−4)−3(2k−1) .(1 point)
Responses

8k−11
8 k minus 11

−4k−5
negative 4 k minus 5

−6k−18
negative 6 k minus 18

−4k−11

Answer 9

To simplify the expression \( 2(k - 4) - 3(2k - 1) \), we will first distribute the constants across the terms in the parentheses.

1. Distributing: \[ 2(k) - 2(4) - 3(2k) + 3(1) \] This becomes: \[ 2k - 8 - 6k + 3 \]

2. Now, combine like terms:

   • Combine the \( k \) terms: \( 2k - 6k = -4k \)
   • Combine the constant terms: \( -8 + 3 = -5 \)

So, the expression simplifies to: \[ -4k - 5 \]

Out of the provided options, the correct answer is: \(-4k - 5\).