Question

What is the value of x in the equation 2(x – 3) + 9 = 3(x + 1) + x?

Answer 1

2(x – 3) + 9 = 3(x + 1) + x
2x - 6 + 9 = 3x + 3 + x
2x + 3 = 4x + 3
-2x -2x

2x + 3 = 3
- 3 -3

2x = 0
x = 0

Answer: The value of x is 0

Answer 2

Given the equation:
`2(x-3)+9=3(x+1)+x`

Distributive property of multiplication states that when a number is multiplied by the sum of the two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately i.e,

`a \cdot (b+c) = a\cdot b+a\cdot c`

Now, using distributive property to LHS and RHS, we get

`2x-6+9=3x+3+x`

Combine like terms on RHS;

`2x-6+9 = 4x+3`

or

`2x+3 = 4x+3`

Subtract 3 from both sides of an equation;

2x+3-3 =4x+3-3

Simplify:

2x = 4x

or

`4x-2x =0`

2x = 0

⇒ x =0

Therefore, the value of x in the given equation

`2(x-3)+9=3(x+1)+x` is 0.