Answer:
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Step-by-step explanation:
![4(1-x)+2x=-3(x+1)](https://tex.z-dn.net/?f=4%281-x%29%2B2x%3D-3%28x%2B1%29)
<u>Distribute</u> 4 through the parentheses
![4-4x+2x=-3(x+1)](https://tex.z-dn.net/?f=4-4x%2B2x%3D-3%28x%2B1%29)
<u>Distribute</u> -3 through the parentheses
![4-4x+2x=-3x-3](https://tex.z-dn.net/?f=4-4x%2B2x%3D-3x-3)
Collect like terms
![-4x+2x](https://tex.z-dn.net/?f=-4x%2B2x)
Collect <u>like terms</u> by calculating the sum or difference of their <u>coefficient</u>
<u></u>
<u></u>
<u></u>
Calculate the sum
![-2x](https://tex.z-dn.net/?f=-2x)
![4-2x=-3x-3](https://tex.z-dn.net/?f=4-2x%3D-3x-3)
Move variable to the left hand side and change its sign
![4-2x+3x=-3](https://tex.z-dn.net/?f=4-2x%2B3x%3D-3)
Why move an expression to the right?
We want to move an expression to the right to write the equation in a specific way.
The opposite needs to be added to both sides to preserve the relation between the sides. That is called the addition and subtraction property of equality/inequality
Step 1
Example
take the equation:
![x+a=b](https://tex.z-dn.net/?f=x%2Ba%3Db)
We want the expression a to be on the right hand side of the equation.
Step 1
example(cont)
To move the expression to the right -hand side, use the addition property , and add -a to both sides of the equation:
![x+a+(-a)=b+(-a)](https://tex.z-dn.net/?f=x%2Ba%2B%28-a%29%3Db%2B%28-a%29)
Simplify the left hand side and remove the parentheses on the right hand side:
![x+a+(-a)=b+(-a)\\x=b-a](https://tex.z-dn.net/?f=x%2Ba%2B%28-a%29%3Db%2B%28-a%29%5C%5Cx%3Db-a)
Now the expression a is on the right hand side :
![x=b-a](https://tex.z-dn.net/?f=x%3Db-a)
Step 2:
Notice! when comparing the beginning and the ending equation, it seems like we just moved the expression to the right hand side and changed its sign:
![x+a=b\\x=b-a](https://tex.z-dn.net/?f=x%2Ba%3Db%5C%5Cx%3Db-a)
This is a shorter way to use the same property.
Now came back to the original equation
![4-2x+3x=-3](https://tex.z-dn.net/?f=4-2x%2B3x%3D-3)
Move <u>constant</u> to to the right hand side and change its sign
![-2x+3x=-3-4](https://tex.z-dn.net/?f=-2x%2B3x%3D-3-4)
collect like terms
![x=-3-4](https://tex.z-dn.net/?f=x%3D-3-4)
calculate the difference
![x=-7](https://tex.z-dn.net/?f=x%3D-7)
Why move a constant to the right?
We want to move a constant to the right because the mathematicians agreed upon a convention that the constants in the equation and inequalities always need to be on the right-hand side.
The opposite needs to be added to both sides to preserve the relation between the sides. That is called the addition and subtraction property of equality/inequality.
Step 1
example
Take the equation:
![x+3=5](https://tex.z-dn.net/?f=x%2B3%3D5)
We want the constant 3to be on the right hand side of the equation.
Step 1
example (cont)
To move the constant to the right-hand side, use the addition property, and add -3 to both sides of the equation:
![x+3+(-3)=5+(-3)](https://tex.z-dn.net/?f=x%2B3%2B%28-3%29%3D5%2B%28-3%29)
Simplify the left-hand side and remove the parentheses on the right - hand side:
![x+3+(-3)=5+(-3)\\x=5- 3](https://tex.z-dn.net/?f=x%2B3%2B%28-3%29%3D5%2B%28-3%29%5C%5Cx%3D5-%203)
Now , all the constants are on the right- hand side:
![x=5-3](https://tex.z-dn.net/?f=x%3D5-3)
Step 2
Notice! when comparing the beginning and the ending equation, it seems like we just moved the constants to the right hand side and change its sign:
![x+3=5\\x=5-3](https://tex.z-dn.net/?f=x%2B3%3D5%5C%5Cx%3D5-3)
This is a shorter way to use the same property.
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