word problem on algebra one variable equations

Most of the 7th grade math equations will have this kind of equations with just one variables,before we go deep into this ,let's see what is a variable means.

Varying, in the context of mathematical variables, does not mean change, but rather, dependence on the values of other variable in the expression in which the variable occurs, or dependence of the value of the expression on that of the variable. However, in some languages other than English, one distinguishes between "variables" in functions and "unknown quantities" in equation

Here is a example from algebra 1 word problems

Question:-

The half life of a radioactive substance is 5750 years.If the mass of a sample is 240 after 5000 year.find its initial mass

Answer:-

Let the initial mass be x. It can be solve by algebra calculator online variables,but
now we are finding this value manually as follows

Then current mass 240 is given by

240 = x (1/2)^5000/5750

= x (0.5)^0.87

= x(0.547)

x = 240/0.547 =438.76

The initial mass was 438.76 units.

A problem on QUADRATIC EQUATION

Topic : Quadratic Equation

An equation of the form ax²+bx+c=0 where a, b, c are real numbers and a ≠ 0, is called a quadratic equation.

Question: The standard form of quadratic equation is ax²+bx+c = 0. Where a and b are co-efficient of x and c is a constant. Find the factors of quadratic equation?

Answer:
1^stmethod----> Find the factors of (a * c) such that addition or subtraction of
that factor is the middle term b.
2^ndmethod----> using quadratic formula

-b + √ b2 - 4ac
_______________
      2a

Example of 1^stmethod
x² + 5x + 6 = 0
Here a = 1, b = 5, c = 6
x² + 5x + 6 = 0
x2 +2x + 3x + 6 = 0
x(x + 2) +3 (x + 2) = 0
(x + 2) (x + 3) = 0
x + 2 = 0 or x + 3 = 0
x = - 2 or x = - 3
or x = -2 , -3