# Math

posted by .

40-3n=-23
what is n?

2/3-6h=-13/6
what is h?

write as a equation,then solve.

the quotient of a number and 2, minus 9, is 14

a number decreased by 7 and then divided by 5 is 13

the sum of 15 and 7 times a number is 99

• Math -

I assume you are just learning this basic algebra.
The general concept in solving equations is this:
"Whatever you do (arithmetic operation) to one side, you must do to the other side.
In general, the object is to get all the variable terms to one side, and the constants to the other side.

40 - 3n = -23

subtract 40 from both sides and simplify

40 - 3n - 40 = -23 - 40
-3n = -63
divide both sides by -3

-3n/-3 = -63/-3
n = 21

2/3 - 6h = -13/6
often it is a good idea to get rid of fractions.
the LCD of all the terms is 6, so multiply each term by 6
(2/3)(6) - 6h(6) = (-13/6)(6)
4 - 36h = -13 , ahhh, no more fractions
4 - 36h - 4 = -13 - 4
-36h = -17
divide by -36

h = 17/36

To change a "word problem sentence " into an equation , just translate it

I will do the second of your questions.

"a number decreased by 7 and then divided by 5 is 13 "
let the number be x
(x - 7)/5 = 13 , notice I just translated the English into Math
multiply both sides by 5
x-7 = 65
add 7 to both sides
x = 72

check:
subtract 7 form 72 ---> 65
divide that by 5 ---> 13
YEahhh!

try the others the same way,
(check your answer by following the wording of the problem. That way you are sure you have the right answer.)

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