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
what is the LCD for 3/5-2/10
To find the value of "n" in the equation 40 - 3n = -23, you need to isolate the variable "n".
1. Start by moving the constant term (-23) to the other side of the equation by adding 23 to both sides:
40 - 3n + 23 = -23 + 23
63 - 3n = 0
2. Next, you want to isolate the variable "n" by eliminating the constant term. You can do this by subtracting 63 from both sides:
63 - 3n - 63 = 0 - 63
-3n = -63
3. Finally, to solve for "n", divide both sides of the equation by -3:
-3n / -3 = -63 / -3
n = 21
So, in the equation 40 - 3n = -23, n = 21.
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To find the value of "h" in the equation 2/3 - 6h = -13/6, you need to isolate the variable "h".
1. Start by moving the constant term (-13/6) to the other side of the equation by adding (13/6) to both sides:
2/3 - 6h + 13/6 = -13/6 + 13/6
2/3 - 6h + 13/6 = 0
2. Next, you want to isolate the variable "h" by eliminating the constant term. To do this, you need to have a common denominator. So, multiply the first term by 2/2 and the second term by 3/3:
(2/3) * (2/2) - 6h + (13/6) * (3/3) = 0
4/6 - 6h + 39/18 = 0
3. Simplify the equation:
2/3 - 6h + 13/6 = 0
4/6 - 6h + 39/18 = 0
4/6 + 39/18 - 6h = 0
(12/18 + 39/18 - 6h) = 0
(51/18 - 6h) = 0
4. Combine like terms on the left side:
(51 - 6h) / 18 = 0
5. To solve for "h", multiply both sides of the equation by 18 to eliminate the fraction:
18 * [(51 - 6h) / 18] = 0 * 18
51 - 6h = 0
6. Finally, isolate the variable "h" by moving the constant term (51) to the other side of the equation by subtracting 51 from both sides:
51 - 6h - 51 = 0 - 51
-6h = -51
7. Solve for "h" by dividing both sides of the equation by -6:
-6h / -6 = -51 / -6
h = 8.5
So, in the equation 2/3 - 6h = -13/6, h = 8.5.
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Let's write and solve the equations for the remaining problems:
1. The quotient of a number and 2, minus 9, is 14.
Translation: (x / 2) - 9 = 14
To solve for "x", isolate the variable by adding 9 to both sides:
(x / 2) - 9 + 9 = 14 + 9
(x / 2) = 23
Multiply both sides of the equation by 2:
2 * (x / 2) = 2 * 23
x = 46
So, the number is 46.
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2. A number decreased by 7 and then divided by 5 is 13.
Translation: (x - 7) / 5 = 13
To solve for "x", isolate the variable by multiplying both sides by 5:
5 * [(x - 7) / 5] = 5 * 13
x - 7 = 65
Add 7 to both sides to isolate "x":
x - 7 + 7 = 65 + 7
x = 72
So, the number is 72.
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3. The sum of 15 and 7 times a number is 99.
Translation: 15 + 7x = 99
To solve for "x", isolate the variable by subtracting 15 from both sides:
15 + 7x - 15 = 99 - 15
7x = 84
Divide both sides of the equation by 7:
7x / 7 = 84 / 7
x = 12
So, the number is 12.
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.)