Answer:
- This statement is given.
- Add 2 to both sides of this equation.
- Add [tex]-4x[/tex] to both sides of this equation.
- Divide both sides by 2.
- Apply the symmetric property of equality.
Step-by-step explanation:
The unknown [tex]x[/tex] and the numbers are mixed in the given equation. However, in the desired equation, the left-hand side contains only the unknown while the right-hand side contains only numbers.
Start with the given equation. That's statement 1.
The question chooses to move the number [tex]-2[/tex] from the right-hand side of the equation to the left-hand side in statement 2. This change can be done by adding [tex]2[/tex] (the opposite of [tex]-2[/tex]) to both sides of the equation.
In statement 3, The question moves the term with the unknown [tex]4x[/tex] from the left-hand side of the equation to the right-hand side. This change can be done by adding [tex]-4x[/tex] (the opposite of [tex]4x[/tex]) to both sides of the equation.
The coefficient of the unknown [tex]x[/tex] in statement 3 is [tex]2[/tex]. In statement 4, the question turns this coefficient into [tex]1[/tex]. This change can be done by dividing both sides by the coefficient of [tex]x[/tex]. Keep in mind that multiplying both sides with the reciprocal of that coefficient, [tex]1/2[/tex], will achieve the same effect.
By the symmetric property of equality, [tex]a = b[/tex] if and only if [tex]b = a[/tex]. In other words, if [tex]3/2 = x[/tex] is true, [tex]x = 3/2[/tex] must also be true. That leads to statement 5.
