Question

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Answer 1

$\rm{6-3(2 x-3)=5(3-x)+2 x}$

Simple numerical terms are commonly written last.

$\to\rm{-3(2 x-3)+6=5(-x+3)+2 x}$

We need to expand this term by multiplying a term and an expression. Product distributive property will be used to do it : a(b + c) = ab + ac

$\to\rm{-(3 \cdot 2 x-3 \cdot 3)+6=(-5 x+5 \cdot 3)+2 x}$

Numerical factors in this term have been multiplied.

$\to\rm{-(6 x-9)+6=(-5 x+15)+2 x}$

We need to get rid of expression parentheses. If there is a negative sign in front of it, each term within the expression changes sign.  Otherwise, the expression remains unchanged.

$\to\rm{-6 x+9+6=-5 x+15+2 x}$

Numerical terms in this expression have been added.

$\to\rm{-6 x+15=-5 x+2 x+15}$

We need to combine like terms in this expression by adding up all numerical coefficients and copying the literal part, if any.  No numerical coefficient implies value of 1.

$\to\rm{-6 x+15=-3 x+15}$

We need to remove equivalent terms that are found on both sides of this equation.

$\to\rm{-6 x=-3 x}$

In order to solve this linear equation, we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. Notice that a term changes sign when it 'moves' from one side of the equation to the other.

$\to\rm{-6 x+3 x=-3 x+3 x}$

We need to combine like terms in this expression by adding up all numerical coefficients and copying the literal part, if any.  No numerical coefficient implies value of 1.

$\to\rm{-3 x=0}$

We can get rid of the negative sign on the left side, since the right side is equal to zero.

$\to\rm{\dfrac{3 x}{3}=0}$

We need to reduce this fraction to the lowest terms.  This can be done by dividing out those factors that appear both in the numerator and in the denominator.

$\boxed{\rm{\to x=0}}$

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Verification :

$\rm{6-3(2 x-3)=5(3-x)+2 x}$

Substitute The Value of x into the Expression

$\to\rm{6-3[(2\times 0)-3]=5(3-0)+2\times 0}$

Apply Rule : n × 0 = 0

$\to\rm{6-3(0-3)=5(3-0)+0}$

Apply Rule : 0 - n = - n and n - 0 = n

$\to\rm{6-3(-3)=5(3)+0}$

$\to\rm{6-(-9)=5(3)+0}$

Apply Plus Minus Rules

$\to\rm{6+(9)=15+0}$

Remove parentheses

$\to\rm{6+9=15+0}$

Simplify the Expression

$\to\rm{15=15}$

• We showed that Two Sides Could Take Same Form (Equal Form)

Hence our Answer x = 0 is Correct

Answer 2

S O L U T I O N

6 − 3(2x − 3) = 5(3 − x) + 2x

6 − 6x + 9 = 15 - 5x + 2x

15 − 6x = 15 - 3x

3x − 6x = 3x - 3x

- 3x = 0

x = 0

V E R I F I C A T I O N

6 − 3(2*0 − 3) = 5(3 − 0) + 2*0

6 − 3(0 − 3) = 5(3 − 0) + 0

6 − 3(− 3) = 5(3)

6 + 9 = 15

15 = 15