SOLUTION: The least of three consecutive odd integers is 2 more than half the largest. what are the integers?

Question 389185: The least of three consecutive odd integers is 2 more than half the largest. what are the integers?
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
I wasn't sure if you need the problem set up or solved; I did both.
(2x-1)+(2x+1)+(2x+3)=2+(1)/(2)*(2x+3)
Remove the parentheses that are not needed from the expression.
2x-1+2x+1+2x+3=2+(1)/(2)*(2x+3)
Since 2x and 2x are like terms, add 2x to 2x to get 4x.
4x-1+1+2x+3=2+(1)/(2)*(2x+3)
Since 4x and 2x are like terms, add 2x to 4x to get 6x.
6x-1+1+3=2+(1)/(2)*(2x+3)
Add 1 to -1 to get 0.
6x+3=2+(1)/(2)*(2x+3)
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 2.
6x+3=2*(2)/(2)+(2x+3)/(2)
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 2.
6x+3=(2*2)/(2)+(2x+3)/(2)
Multiply 2 by 2 to get 4.
6x+3=(4)/(2)+(2x+3)/(2)
The numerators of expressions that have equal denominators can be combined. In this case, ((4))/(2) and ((2x+3))/(2) have the same denominator of 2, so the numerators can be combined.
6x+3=((4)+(2x+3))/(2)
Simplify the numerator of the expression.
6x+3=(4+2x+3)/(2)
Add 3 to 4 to get 7.
6x+3=(7+2x)/(2)
Reorder the polynomial 7+2x alphabetically from left to right, starting with the highest order term.
6x+3=(2x+7)/(2)
Multiply each term in the equation by 2.
6x*2+3*2=(2x+7)/(2)*2
Simplify the left-hand side of the equation by multiplying out all the terms.
12x+6=(2x+7)/(2)*2
Simplify the right-hand side of the equation by simplifying each term.
12x+6=2x+7
Since 2x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2x from both sides.
12x+6-2x=7
Since 12x and -2x are like terms, add -2x to 12x to get 10x.
10x+6=7
Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.
10x=-6+7
Add 7 to -6 to get 1.
10x=1
Divide each term in the equation by 10.
(10x)/(10)=(1)/(10)
Simplify the left-hand side of the equation by canceling the common factors.
x=(1)/(10)
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