Question

Justify Solution Paths of Linear Equations

3(x−2)+5x=26 (What property is this?)
3x−6+5x=26 (What property is this?)
8x−6=26 (What property is this?)
8x=32 (What property is this?)
x=4 (What property is this?)


Here are a list of the properties-

Subtraction Property of Equality
Addition Property of Equality
Multiplication Property of Equality
Division Property of Equality
Combine Like Terms
Distributive Property
Given Equation

Answer 1

`3(x-2)+5x=26` (Given Equation)

`3x-6+5x=26` (Distributive Property)

`8x-6=26` (Combine Like Terms)

`8x=32` (Addition Property of Equality)

`x=4` (Division Property of Equality)

Explanation:

To justify the solution paths of linear equations.

`3(x-2)+5x=26` (It is the Given Equation)

Here, 3 has to be multiplied with the term
`(x-2)`, so the distributive property applies.

Therefore,
`3x-6+5x=26`

Here, the like terms with
`x` in it will have to solved by combining them into one.

Therefore,
`8x-6=26`

Here, we add 6 to both sides.

`8x=32`

Now, divide the both sides with 8.

`x=4`

Therefore, the answer is:

`3(x-2)+5x=26` (Given Equation)

`3x-6+5x=26` (Distributive Property)

`8x-6=26` (Combine Like Terms)

`8x=32` (Addition Property of Equality)

`x=4` (Division Property of Equality)