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Answer:
[tex]-12[/tex]
Step-by-step explanation:
Let that number be [tex]x[/tex]. We can build an equation, and solve for [tex]x[/tex].
[tex]4[/tex] less than half of [tex]x[/tex] is [tex]x/2-4[/tex].
[tex]2[/tex] more than [tex]x[/tex] is [tex]x+2[/tex].
We are given that the two quantities are equal, so we have that [tex]x/2-4=x+2[/tex].
Adding [tex]4[/tex] to both sides gives [tex]x/2=x+6[/tex].
Multiplying both sides by [tex]2[/tex] gives [tex]x=2(x+6)=2x+12[/tex].
Subtracting [tex]2x[/tex] from both sides gives [tex]-x=12[/tex].
Multiplying both sides by [tex]-1[/tex] gives [tex]x=-12[/tex].
So, the number is [tex]\boxed{-12}[/tex] and we're done!
The check is left as an exercise to the reader.