Often whether it is a student learning science or a businessman crunching business numbers, they often come across algebra expressions and need to solve them to know the unknown. In this article, let us see how we solve the algebraic expressions.
Algebra is the branch of mathematics that involves the study of letters and symbols which represent unknown numbers or quantities, which are then solved for and manipulated in various ways. When we write algebraic expressions such as “x+3” or “x-y”, what we are doing is writing out a mathematical statement in an abbreviated form. Algebraic expressions are solved by combining like terms together and then using the order of operations to solve for the unknown variable.
The article below will show you everything from how algebra in math works to examples of them in use.
It is important to note that there is not one specific way to solve algebraic expressions, and one can follow any logic to find the value of the unknown variables. The idea is to simplify the expression and do the arithmetic operations on like terms in the equation, and thereafter comes the idea of substitution. We will learn some of the tricks to solve algebraic expressions below but keep in mind again that these are not the only way to solve them.
Single variable algebraic expressions have only one variable present in them.
For example, 3x + 2 = 5 has only one variable, ‘x,’ which, when multiplied by 3 and added with number 2, gives the number 5. For this expression, we can see that when the value of x is 1, it satisfies the equation. So, for this very simple expression, one can simply see what the value of the variable is.
Lets us consider a more complicated example, like 3x + 2 = 5x – 8
Now, move the like terms to one side of the equation, so we re-arrange the equation as
8 + 2 = 5x – 3x
Note how the sign of the operand changes as it moves to the other side of the equal sign.
Solving the arithmetic on both sides of the equation gives us 10 = 2x and so the value of x = 5
Let us consider an equation with two variables, like 2x + 3y = 6x – y
Now to find the value of x and y, we would need one more equation. Here we come across a very useful rule to remember that to find the value of ‘n’ number of variables, we need ‘n’ number of equations. So lets add one more equation like 9x + 6 = 15y
By moving the like terms of the first equation to one side of the equal to sign, we get
y + 3y = 6x – 2x
4y = 4x
y = x
So, now we can substitute y with x in the second equation.
9x + 6 = 15y
9x + 6 = 15x
6 = 15x – 9x
6 = 6x
x = 1
And as we know, x = y; hence the value of y is also 1.
Above we took examples where the variables did not have any exponent power. There is a very commonly used algebraic expression called quadratic equations, which have one variable with square power. Let’s see an example of a quadratic equation.
x2 + 7x + 12
First, we need to try and factorize this equation by breaking the term having a single power of the variable. So by breaking 7x as 3x + 4x, we can rewrite the equation as,
x2 + 3x + 4x + 12
x (x+3) + 4 (x+3)
(x + 3) (x + 4) = 0
So, x is -3 and x is also -4.
For more clarity and tips and tricks on algebra, students can refer to alternate resources online and offline as well as expand their understanding. One such online platform is Cuemath which provides plenty of educational resources like math worksheets on several topics for the students to practice and enhance their math skills. There are also online math tutors available there in case students would require extra help on any topic.