How to Use Algebra in Real Life Situations

Linear Equations and Inequalities 

3x+5=17 

3x=17-5 

3x=12 

x=12/3 

x=4 

Therefore, the solution is x=4. 

4x-5>20 

4x>20+5 

4x>25 

x>25/4 

x>6.25 

Therefore, x > 6.25 

2-x=12 

-x=10 

x=10/-1 

x=-10 

So the answer is x= -10. 

3-2x < 5x-10 

The terms are first reordered 

3 - 2x <-10 + 5x 

The above problem can then be solved by adding 10 on both sides 

3 – 2x + 10 < -10 + 5x + 10 

13 – 2x < 5x 

13<5x+2x 

13 < 7x 

X >13/7 

X can be simplified as follows 

X > 13/7 

X >1.857 

Therefore x > 13/7 or x > 1.857 

Multiplication 

To multiply (2x+3) (3-x) 

2x(3-x) + 3(3-x) 

6x-2x 2 + 9-3x 

6x-3x-2x 2 +9 

3x-2x 2 +9 

Rearrange the terms in the standard form of ax 2 +bx+c 

-2x 2 +3x+9 

Multiply each term by -1 

2x 2 -3x-9 

To multiply (4-x) (5-x) 

4(5-x) – x(5-x) 

20-4x-5x+x 2 

20-9x+x 2 

Rearrange the equation in the form of ax 2 +bx+c 

x 2 -9x+20 

Factor Expressions 

To factor 9x 2 +6x+1 

To the factor, a quadratic expression ax 2 +bx+c, rewrite the equation such that b is a sum of two numbers n1 and n2, where n1*n2=a*c and n1+n2=b 

9x 2 +3x+3x+1 

Group the terms into pairs 

(9x 2 +3x) + (3x+1) 

Factor out the common terms from each pair,3x and 1 

3x(3x+1) + 1(3x+1) 

(3x+1) (3x+1) 

Factor using the perfect square trinomial rule a 2 -2ab+b 2 =(a-b) 2 

(x-4) 2 

Therefore, the factor of 9x 2 +6x+1 is (x-4) 2 

To factor 16-8x+x 2 

Rewrite the quadratic in the standard form ax 2 +bx+c 

x 2 -8x+16 

Rewrite the equation such that b is a sum of two numbers n1 and n2, where n1*n2=a*c and n1+n2=b 

x 2 -4x-4x+16 

Group the terms into pairs 

(x 2 -4x) – (4x+16) 

Factor out the common factors from each pair, x and 4 

x(x-4) – 4(x-4) 

(x-4) (x-4) 

Factor using the perfect square trinomial rule a 2 -2ab+c=(a-b) 2 

(x-4) 2 

Therefore, the factor of 16-8x+x 2 is (x-4) 2 

Application of Algebra in Real-Life Situations 

Whenever we encounter mathematical expressions with unknown values, the first question that runs through our minds is how the expressions are applicable in real-life situations. Because human beings often deal with problems that require decision-making, such problems can easily be resolved by reducing them into simple mathematical expressions, inequalities, or equations. Solving the equations, for instance, it results in the resolution of the problem because the answer applies to the problem upon which the expression was formulated. In real life, there are a lot of jobs whose execution requires the application of this mathematical knowledge. A critical look at the application of Algebra in a real-life situation is therefore required. The following section discusses some of the situations that algebra can be used in real life. 

Allocation of Resources by the Government 

The government has been bestowed with the responsibility of collecting revenue from the people in the form of taxes for development purposes. Once obtained, the income had to be directed into projects and used to provide the much-needed services that are of benefit to the people in an equitable manner. Besides, based on the needs the government has to work with projections on revenue to aid in budgeting (Glazer & McConnell, 2002). In making such decisions, the problems are quickly resolved by reducing them to simple algebraic expressions on which mathematical knowledge is applicable. 

Business and algebra 

One of the primary reasons for the existence of companies is to make a profit from their operations. For this to be achieved, informed decisions have to be made from time to time. For instance, companies involved in the manufacturing of goods have to ensure that their products are sold at a higher price than the total cost incurred in production to realize a profit (Glazer & McConnell, 2002). Similarly, companies operating in different lines of production have to decide on how to direct their resources within the business. Profitable production lines often receive the highest share of the resources. According to Snyder, (2018), when businesses present such problems that call for decision-making, reducing the issues to simple inequalities and using mathematical knowledge makes decision-making easier. 

Long-term investments 

Most people run a retirement plan or an insurance policy with the aim of saving for the future, with contributions towards the plans made either monthly or annually. The application of knowledge in quadratic functions makes it possible to project the total contributions and interest at the end of a given period. This, in turn, determines the monthly contribution. Similarly, this applies to businesses that intend to venture into long-term investments (Glazer & McConnell, 2002). 

Unit conversions 

Different countries, for instance, use their currencies to transact domestically. When traveling from one country to another requires one to convert to the currency acceptable in that country. The process of conversion is in itself the application of knowledge in linear functions because the currency units are linearly related (Glazer & McConnell, 2002). 

Estimation of rates, distance, and time 

In recent times, many countries and organizations are involved in research to ascertain whether life is supported on other planets for example. When launching rockets from the earth, the application of equations is paramount in determining the ideal velocity the rocket will break the gravitational pull of the planet (Glazer & McConnell, 2002). Similarly, linear functions are applicable where people might be intending to go for a road trip. Approximations can be made on the time of arriving at the intended destination by giving insights on the time of departure in consideration of other factors such as traffic on the selected route (Glazer & McConnell, 2002). 

In light of this, the importance of mathematical knowledge cannot be overemphasized. The process used in solving equations and expressions gives an understanding of how important and applicable it is in the resolution of real-life problems. Although not all issues can be converted into mathematical equations and expressions, it is knowledge that plays the most significant role in solving emerging problems. 

References 

Glazer, E., & McConnell, J. (2002).  Real-life math . Westport, Conn.: Greenwood Press. 

Snyder, M. (2018). Retrieved from https://sciencing.com/10-can-used-everyday-life-8710568.html