Answer:
Equation: [tex]\large\sf\:\frac{x\:-\:5}{2}\:=\:-2[/tex]
Step-by-step explanation:
Given the expression, "Half the difference of a number and 5 is -2" can be represented algebraically.
In order to make it easier to understand what the equation represents the given sentence, we must break it down into smaller portions.
Let x = a number.
In the phrase, "... difference of a number and 5" is the same as: x - 5.
Finally, given the phrase, "Half the difference of a number and 5 is -2" is the same as: [tex]\large\sf{\frac{1}{2}\:of\:x\:-\:5\:=-2}\\[/tex].
However, it is more appropriate to express the given statement in the following equation:
[tex]\large\sf\:\frac{x\:-\:5}{2}\:=\:-2[/tex] ⇒ This is the equation that represents the given statement.
Bonus: Solving for the value of x:
If we actually solve for x, what we could do is to first multiply both sides by 2 in order to eliminate the fraction on the left-hand side:
[tex]\large\sf\:\frac{x\:-\:5}{2}(2)\:=\:-2(2)[/tex]
x - 5 = -4
Finally, add 5 to both sides to solve for x:
x - 5 + 5 = -4 + 5
x = 1
Substituting the value of x into the equation:
[tex]\large\sf\:\frac{x\:-\:5}{2}\:=\:-2[/tex]
[tex]\large\sf\:\frac{1\:-\:5}{2}\:=\:-2[/tex]
[tex]\large\sf\:\frac{-4}{2}\:=\:-2[/tex]
-2 = -2 (True statement). Therefore, we have the correct value for x.
