Question

How do you solve `-3x + 7= - x -`?

Answer 1

Consider the given equation as meant to be: `-3x+7=-x`

Thus: `x=7/2`

Explanation:

`color(blue)("Assumption: The given equation format is correct:")` The instruction is to determine the value of ?

As it is preceded by the mathematical instruction of 'subtract' (minus) it has to be valid part of the given equation.

For now write the variable `b` instead of ?. I am more comfortable with that format as the use of ? as a valid symbol for a finished equation is rather unusual.

Add `color(red)(x)` to both sides

`color(green)(-3xcolor(red)(+x)+7" "=" "-xcolor(red)(+x)-b)`

`-2x+7" "=" "-b`

Multiply everything by (-1) to make the `x` term positive.

`+3x-7" "=" "+b`

Add 7 to both sides

`3x" "= "b+7`

Divide both sides by 3

`x" "=" "1/3(b+7)`

Thus the solutions for `x` is an infinite set of values

NOT VERY LIKELY THE INTENDED ANSWER.

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`color(red)("Assumption: The given equation format is not correct:")`

Consider as meant to be: `-3x+7=-x`

Add `x` to both sides

`-2x+7=0`

Multiply everything by -1

`+2x-7=0`

Add 7 to both sides

`2x=7`

Divide both sides by 2

`x=7/2`