solving equations with integers.
An equation is an expression mathematics related to the = sign on which letters are called unknowns and the goal is to find a value for the unknown that makes the condition of equality.
EG
x + 5 = 0
must find a value for the unknown. The unknowns can be expressed by any letter, usually using the X, Y, or Z.
This value is: x = -5
because if the replacement would for -5 x:
-5 + 5 = 0
When x = -5 equality holds if, for example, since x = -4 would not be met:
-4 + 5 = 0
1 = 0 NOT MET EQUAL
then said that solution to the equation x + 5 = 0 is: x = -5
equivalent equations:
Two equations are equivalent when they have the same solutions, for example: 5x = 4x +3, is equivalent to 5x-4x = 3; because if we replace them both for x = 3, monitor compliance, both equalities, we see for the first:
For the second:
simple equations are solved by transforming them into equivalent, as a consequence of the law of uniformity of operations with whole numbers, that does not explain at this point, just give a few practical rules for solving equations.
LAW PRACTICE:
order to find the solution of an equation is what is called clearing the xo is leave it alone for a member of equality.
A) When x is accompanied by numbers that are adding or subtracting them then passed to another member with the operation inversely with operating.
EXAMPLE 1:
x + 4 = 2 We spent 4 to another member of the equality but because what we're adding subtracting.
x = 2 to 4 We count and we have
x = -2
Verification:
To see if the solution is correct replace the value of x in the equality
-2 + 4 = 2 2 = 2
EXAMPLE 2:
x + 2 - 3 = 4 + 5 spent the 2 that passes as is adding subtracting
x - 3 = 4 + 5 to 2 3 to spent the rest go as it is adding
x = 4 + 5 - 2 + 3 We account X = 10
Verification: To verify replacement
into the equation the value found
10 + 2 - 3 = 4 + 5 9 = 9
the solution is verified.
EXERCISE:
1) 3 + 2 - 5 + x = 2 + 1 - 3 x = 0
2) -2 + 6 -12 = x + 5 - 1 x = -12
3) 2 + 6 - 1 = x + 6 - 4 x = 5
4) -5 - 6 + x = 5 - 8 + 3 x = 11
5) 6 - 9 + x + 9 = 2 to 6 x = -10
6) 6 - 9 - 3 = 4 + x +3 - 5 x = -8
7) 2 + 5-9 = 2 + x - 6 - 8 x = 10
8) 2 + 9 + 6 - 9 = x + 3 - 5 x = 10
9) 9 - 5 + 6 + x = -5 -9 +3 x = -21
B) When the question is multiplied or divided by a number, it passes to another member or the reverse happens if you multiply by dividing and multiplying if splitting passes.
EXAMPLE 1:
2 x = 4 We
dividing the 2 x = 4: 2 solve x = 2
Verification:
To see if the solution is correct replace the value of x in the equality
2. 2 = 4 4 = 4
is verified
EXAMPLE 2:
-2 x = 4 CUIDADDO! Dividing the -2 passes with his sign because it is multiplied and the inverse operation is division.
x = 4: (-2) x = -2 solve
Verification:
To see if the solution is correct replace the value of x in the equality
-2. (-2) = 4 4 = 4
is verified
EXAMPLE 3:
x: 2 = 4 We
multiplying the 2 x = 4. 2 solve x = 8
Verification:
To see if the solution is correct replace the value of x in the equality
8: 2 = 4 4 = 4
is verified
EXAMPLE 4:
x: (- 2) = 4 CUIDADDO! The multiplying passes -2 its sign because it is divided and the inverse operation is multiplication
x = 4. (-2) X = -8
resolve
Verification:
To see if the solution is correct replace the value of x in the equality
-8. (-2) = 4 4 = 4
is verified
Fitness:
1) 2 x = -4
2) x (-3) = 6
3) -3. x = 18
4) x. (-4) = 16
5) x (-5) = -4
6) 3 x = 9
7) 5 x = 25 x = -2
x = -18 x = -6
x = -2 x = 20
x = 3 x = 5
C) When the mystery is being multiplied and divided by a number and also added to or subtracted from another, first passed the numbers add up or subtracted and then to multiply or divide.
EXAMPLE 1:
2x + 3 - 1 = 6 spent on 3 and 1 adding subtracting
2x = 6 - 3 + 1
Resolved 2x = 4 on 2 passing dividing
x = 4: 2 x = 2
Verification: To verify replacement
into the equation the value found
2. 2 + 3 - 1 = 6
4 + 3 - 1 = 6 6 = 6
the solution is verified.
D) Where there are several unknowns equation multiplied or divided by a number of a member of equality and the other, together with addition or subtraction of numbers. Separated in terms of both sides of equality, and transposed to a member of equality, the numbers multiply the unknown, and the other, the numbers alone. Example: Step
, separated in terms of:
On 2 and 3 which are positive in the first member of equality, step by subtracting from the second:
The negative 5x in the second member, the first positive step: Sumo
the x of the first member, and the numbers of second: 3 will
Then the dividing step, and I have x = 6 / 3, x = 2
Check:
back
Exercises:
Solve the following equations and verify the solution found:
1) 4x-2 = 10 2) 6x-3 = x +17 3) 2x +5 = 3
4) 7x = 4x +6 5) 2x = 9 + x 6) 6x = 24-2x
7) 10 = 15-5x 8) x-8 = 4-x 9) 3x-10 = 18-x
10) 7x-8 = 3x +4 11) 2-3x-5 = 5-8x + x 12) x +2 = 3-2x +8
ANSWERS 1) x = 3 2) x = 4 3) x =- 1
4) x = 2 5) x = 9 6) x = 3
7) x = 1 8) x = 6 9) x = 7
10) x = 3 11) x = 2 12) x = 3
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