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chychy2003
01.02.2020 •
Mathematics
Anumber is decreased by 3 and then the result is doubled. if the new result is 6 more than half the original number, what is the value of the original number?
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Ответ:
Explanation:
Let "x" represent the "original number".
2(x - 3) = 6 + (1/2)x ; Solve for "x" ;
Multiple the ENTIRE EQUATION (both sides) by "2" ; to get rid of the fraction:
2*{2(x - 3) = 6 + (1/2)x} ;
to get:
4(x - 3) = 12 + x ;
Let us expand the "left-hand side" of the equation:
Note the "distributive property of multiplication" :
a(b - c) = ab - ac ;
a(b +c) = ab + ac ;
So; "4(x - 3)" = 4*x - 4*3 = 4x - 12 ;
Rewrite the equation:
4x - 12 = 12 + x ;
Subtract "x" from EACH side of the equation; and Add "12" to EACH SIDE OF THE EQUATION;
4x - 12 - x + 12 = 12 + x - x + 12 ;
to get:
3x = 24 ;
Now, divide EACH side of the equation by "3" ; to isolate "x" on one side of the equation; and to solve for "x" ;
3x/3 = 24/3 ;
x = 8 .
Ответ: