SOLUTION: three times the sum of a number and 4 is 8 less than one-half the number. write and solve an equation to find the number.

Question 678340: three times the sum of a number and 4 is 8 less than one-half the number. write and solve an equation to find the number.
Found 2 solutions by ReadingBoosters, rm29924:
Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
3(n+4) = n-8
...
multiply the entire equation by 2 to be rid of the fraction
2[3(n+4)] = 2()n-2(8)
6(n+4) = n - 16
...
distribute the 6
6n + 24 = n - 16
...
Group the n variable on the left side alone
6n - n = -16 - 24
...
Combine like terms
5n = -40
...
Divide both sides by 5 to isolate n

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Answer by rm29924(97) (Show Source): You can put this solution on YOUR website!
Let X = a number
three times the sum of a number and 4
the sum of a number and 4 means you add them
x+4
three times means multiply by 3
3(x+4)
8 less than one-half the number
one half the number is 1/2X
8 less means subtract 8
1/2x-8
is means equals so set those equal to each other
3(x+4)=1/2x-8
3x+12=1/2x-8
subtract 3x from both sides
12=-2.5x-8
add 8 to both sides
20=-2.5x
divide both sides by 2.5
x= - 8
plug it back into the equation to check work

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