Option D:
is the correct solution to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Option E:
is the correct solution to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Option F:
is the correct solution to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Explanation:
The expression is ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Let us find the value of x.
![\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D6%28x%2B4%29%20%26%3D20%20%5C%5C6%20x%2B24%20%26%3D20%20%5C%5C6%20x%20%26%3D-4%20%5C%5Cx%20%26%3D-%5Cfrac%7B2%7D%7B3%7D%5Cend%7Baligned%7D)
Now, we shall find the expression that is equivalent to the value ![x=-\frac{2}{3}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B2%7D%7B3%7D)
Option A: ![(20-4) \div 6](https://tex.z-dn.net/?f=%2820-4%29%20%5Cdiv%206)
Simplifying the expression, we have,
![\frac{16}{6}=\frac{8}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B6%7D%3D%5Cfrac%7B8%7D%7B3%7D)
Since,
is not equivalent to
, the expression
is not equivalent to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Hence, Option A is not the correct answer.
Option B: ![16(20-4)](https://tex.z-dn.net/?f=16%2820-4%29)
Simplifying the expression, we have,
![16(16)=256](https://tex.z-dn.net/?f=16%2816%29%3D256)
Since, 256 is not equivalent to
, the expression
is not equivalent to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Hence, Option B is not the correct answer.
Option C: ![20-6-4](https://tex.z-dn.net/?f=20-6-4)
Simplifying the expression, we have,
![20-10=10](https://tex.z-dn.net/?f=20-10%3D10)
Since, 10 is not equivalent to
, the expression
is not equivalent to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Hence, Option C is not the correct answer.
Option D: ![20 \div 6-4](https://tex.z-dn.net/?f=20%20%5Cdiv%206-4)
Using PEMDAS and simplifying the expression, we have,
![$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$](https://tex.z-dn.net/?f=%24%5Cbegin%7Baligned%7D%2820%20%5Cdiv%206%29-4%20%26%3D%5Cfrac%7B10%7D%7B3%7D-4%20%5C%5C%20%26%3D%5Cfrac%7B10-12%7D%7B3%7D%20%5C%5C%20%26%3D-%5Cfrac%7B2%7D%7B3%7D%20%5Cend%7Baligned%7D%24)
Thus,
is equivalent to
, the expression
is equivalent to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Hence, Option D is the correct answer.
Option E: ![\frac{1}{6} (20-24)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D%20%2820-24%29)
Simplifying the expression, we have,
![$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$](https://tex.z-dn.net/?f=%24%5Cbegin%7Baligned%7D%20%5Cfrac%7B1%7D%7B6%7D%2820-24%29%20%26%3D%5Cfrac%7B1%7D%7B6%7D%28-4%29%20%5C%5C%20%26%3D-%5Cfrac%7B4%7D%7B6%7D%20%5C%5C%20%26%3D-%5Cfrac%7B2%7D%7B3%7D%20%5Cend%7Baligned%7D%24)
Thus,
is equivalent to
, the expression
is equivalent to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Hence, Option E is the correct answer.
Option F: ![(20-24) \div 6](https://tex.z-dn.net/?f=%2820-24%29%20%5Cdiv%206)
Simplifying the expression, we have,
![$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$](https://tex.z-dn.net/?f=%24%5Cbegin%7Baligned%7D%2820-24%29%20%5Cdiv%206%20%26%3D-%5Cfrac%7B4%7D%7B6%7D%20%5C%5C%20%26%3D-%5Cfrac%7B2%7D%7B3%7D%20%5Cend%7Baligned%7D%24)
Thus,
is equivalent to
, the expression
is equivalent to the equation ![6(x+4)=20](https://tex.z-dn.net/?f=6%28x%2B4%29%3D20)
Hence, Option F is the correct answer.