# Quality Problem Solving

Introduction :

The solving and learning the math can be done by using some known formulas and some arithmetic operations such as addition,subtraction,division and multiplication.The word quality states that discipline of work .Initially the quality  gives good work Here we are going to see some quality math problems like an algebra problems,geometry problems and fraction problems.The below content shows the quality of problem  solving.
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Math problem 1:

solve the given problem (26x^2 – 29x – 15) + (17x^2 – 23x – 26) – (–52x^2 + 18x + 4)

Solution:

The problem can be solved in simplifying method .

Step 1:(26x^2 – 29x – 15) + (17x^2 – 23x – 26) – (–52x^2 + 18x + 4)

Step 2: 26x^2 – 29x – 15 + 17x^2 – 23x – 26 + 52x^2 `-` 18x `-` 4

Step 3: 26x^2 + 17x^2+52x^2 – 29x– 23x – 18x – 15 –26 – 4.

Step 4: 95 x^2 – 70x –45

(26x^2 – 29x – 15) + (17x^2 – 23x – 26) – (–52x^2 + 18x + 4)  = 95 x^2 – 70x –45

Math problem 2:

Calculate the given equation 26`n` = – 26`n` – 1924 to find the solution for `n`.

Solutions:

Step 1: Consider the given equation,

26`n` = – 26`n` – 1924

Step 2: Add 26 `n` on either side

26`n`+ 26`n` = – 26`n`+ 26 `n` – 1924

Step 3: Simplify the above expression, we get

52`n` =  – 1924

Step 4: Divide by 52 on either side

` (52n)/52 = (-1924)/ 52`

`n = (-1924)/ (52)`

Thus, the solutions for        `n = (-1924)/ (52)`
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Problem 3:

calculate and find  addition of two fraction  `512/45` and `427/53`

Solution:

The given two fractions are `512/45` and `427/53`

Step1: The given two fractions

=   `512/45` + `427/53`

Step 2: Now we need to find the sum of  `512/45` and `427/53`

The LCM of 45 and 53 is 2385

= ` (512xx 53 + 427 xx 45)/2385`

= `(27136+ 19215)/2385`

Step 3:The sum of 27136 and 19215 is 46351

= `46351/2385`

Problem 4:

Find the equation of the point is  (45, 48) and slope is 23

Solutions:

Step 1: Consider the given,

Point (45, 48) ---` x_ (1), y_ (1)`

Slope m = 23

Step 2: The equation of the point slope form is

`y - y_ (1) = m(x - x_ (1))`

Step 3: Plug the point in the point slope form, we get

y – 48 = 23( x − 45)

Step 4: Simplify the expression,

y – 48=23x – 1035

Step 2: Add 48 on either side

y – 48+ 48 = 23x – 1035+ 48

y = 23x – 273.

Thus, the obtained math equation is    y = 6x – 987 .