The answer will be : x = -- 3y -- 9
⇒ -2 (x + 3y) = 18
⇒ -(2x + 2 * 3y) = 18
⇒ -(2x + 6y) = 18
⇒ (-2x -6y) + 6y = 18 + 6y
⇒ -2x -6y + 6y = 6y + 18
⇒ -2x = 6y + 18
⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]
⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]
⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]
⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]
⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]
⇒ x = -[3(y + 3)]
⇒ x = (3y + 3*3)
⇒ x = -(3y + 9)
⇒ x = - 3y - 9
WORKING NOTES :
-2 (x + 3y) = 18
[We must multiply a term and an expression in order to enlarge this word.
We'll utilize the following product distributive property:
A(B + C) = AB + AC
⇒ -(2x + 2 * 3y) = 18
The final expression, in this case, will have two terms:
The first term is a product of '2' and 'x'
the second term is a product of '2' and '3y'.]
In this term, numerical components have been multiplied.
⇒ -(2x + 6y) = 18
We must group all the variable terms on one side of the equation and all the constant terms on the other in order to solve this linear equation.
⇒ (-2x -6y) + 6y = 18 + 6y
Here, the '-' (minus) term, -6y will be moved to the right side.
When a term "moves" from one side of the equation to the other, you'll notice that its sign changes.
Parentheses around expressions must be eliminated.
Each term in the expression changes sign if a negative sign is placed in front of it. Otherwise, the expression stays the same.
There is no negative sign in the situation.
⇒ -2x -6y + 6y = 6y + 18
In order to join like terms in this expression, we must first sum all of the numerical coefficients and, if necessary, replicate the literal section.
Nothing in a number suggests a value of 1.
There is just one set of related terms: -6y, 6y.
⇒ -2x = 6y + 18
We must eliminate the coefficient that multiplies the variable in this linear equation in order to isolate it.
If both sides are divided, then the coefficient must be removed (-2)
⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]
We must simplify this fraction to its simplest form.
To do this, divide the variables that occur in both the numerator and the denominator.
The common factor, in this case, is 2.
⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]
We must consider the GCF (Greatest Common Factor).
The GCF and the original expression, split by the GCF, provide the final term.
⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]
GCF in this case is 2*3.
The fraction [tex]\frac{2*3y}{2*3}[/tex] must be lowered to its simplest form. To do this, divide the variables that occur in both the numerator and the denominator.
Here, the common factor is 2*3.
⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]
The expression must be lowered to its simplest form.
Driving out the components that exist in both the numerator and the denominator will accomplish this.
2*3 is a common factor.
⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]
Numerical terms in the factor {y + (3²⁻¹)} is added which makes it (y + 3)
The fraction will then be broken down into its smallest terms next.
To do this, divide the variables that occur in both the numerator and the denominator.
2 is the common factor.
⇒ x = -[3(y + 3)]
⇒ x = -(3y + 3*3)
We must multiply a term and an expression in order to expand this term.
We'll utilize the following product distributive property:
A=AB+AC = A(B + C)
The final expression, in this case, will have two terms:
"3" and "y" are the product in the first term.
The second term is the result of the numbers 3 and 3.
⇒ x = -(3y + 9)
This term's numerical terms have been multiplied by three (3*3 = 9).
⇒ x = - 3y - 9
The parenthesis around expressions must be eliminated.
Each term in the expression changes sign if a negative sign is placed in front of it.
Otherwise, the expression stays the same.
The signs of the following two terms will now change. -(3y + 9) = - 3y - 9
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