Question

what is the reason for each step in the solution of the equation

18-2x=4x

Drag and drop the reasons into the boxes to correctly complete the table

18-2x=4x

18-6x

3=x

Combine Like Terms

Divison Property of Equality

Addition Property of Equality

Distributive Property

Given

Answer 1

$18-2x=4x$ ⇒ Given

$18-2x-4x=4x-4x$ ⇒ Addition property of equality

$18 - 6x = 0$ ⇒ Combine like terms [-2x-4x = -6x]

$18-6x+6x=0+6x$ ⇒ Addition property of equality

$18=6x$ ⇒ Distributive property

$\frac{18}{6}= \frac{6x}{6}$ ⇒ Division property of equality

$x=3$ ⇒ Answer

Answer 2

Solution of the equation is $x=3$ by writing the reason for each step in the solution of the equation:

Explanation:

Given: Linear equation is $18-2x=4x$

Solving the equation and writing the reason for each step in the solution of the equation:

⇒ $18-2x=4x$                         (Given )

⇒ $18-2x-4x=4x-4x$         (Addition property of equality)  

⇒ $18-6x=0$                           (Combine like terms $[-2x-4x = -6x]$)

⇒ $18-6x+6x=0+6x$           (Addition property of equality)

⇒ $18=6x$                                  (Distributive property)

⇒ $\frac{18}{6}=\frac{6x}{6}$                                  (Division property of equality)

⇒ $3=x$                                     (Answer)

Therefore, the solution of the equation is $x=3$.

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