Question

Charlie used these steps to solve the equation 6x+5=1+2(3x+2). Which choice describes the meaning of his result, 5=5?

Answer 1

Option A is correct

All values of x make the equation true.

Explanation:

Given an equation:

Apply the distributive property to the Right side of the equation

A number is multiplied to the sum of the two numbers, i.e,

then,

or

Subtraction property of equality: Subtract the same number from both sides of an equation.

Subtract 6x from both sides:

Simplify:

or

;

hence the result is true for all values of x.

Answer 2

Option A is correct

All values of x make the equation true.

Explanation:

Given an equation:
`6x+5=1+2(3x+2)`

Apply the distributive property to the Right side of the equation

A number is multiplied to the sum of the two numbers, i.e,
`a\cdot(b+c)=a\cdot b+a \cdot c`

then,

`6x+5=1+2\cdot(3x)+2\cdot 2` or

`6x+5=1+6x+4`

Subtraction property of equality: Subtract the same number from both sides of an equation.

Subtract 6x from both sides:

`6x+5-6x=1+6x+4-6x`

Simplify:

`5=1+4` or

`5=5` ;

hence the result is true for all values of x.